Updated answers to the Titan Test (a phoney IQ test)

[j***@yahoo.com]

If you spot an error or would like to add answers, please reply to this
post or send me an e-mail, or both.
Don't forget to explain your answer, the more detail the better.

The test questions can be found here:
http://www.eskimo.com/~miyaguch/titan.html

1. STRIP : MoBIUS :: BOTTLE : KLEIN

2. THOUGHT : ACTION :: OBSESSIVE : COMPULSIVE

3. LACKING MONEY : PENURIOUS :: DOTING ON ONE'S WIFE : UXORIOUS
(definitions)

4. MICE : MEN :: CABBAGES : KINGS (from literature)

5. TIRE : RETREAD :: PARCHMENT : PALIMPSEST

6. ALL IS ONE : MONISM :: ALL IS SELF : SOLIPSISM (a doctrine in
philosophy, nothing exists except the self, or alternately the
existence of everything else depends on the existence of the self)

7. SWORD : DAMOCLES :: BED : PROCRUSTES

8. THING : DANGEROUS :: SPRING : PIERIAN
(A little learning is a dangerous thing; drink deep, or taste not the
Pierian spring - Alexander Pope. An
Essay on Criticism)

9. HOLLOW VICTORY : PYRRHIC :: HOLLOW VILLAGE : Potemkin

10. PILLAR : OBELISK :: MONSTER : BASILISK (OBELISK from Greek
obeliskos, BASILISK from Greek basiliskos)

11. 4 : HAND :: 9 : SPAN (a hand is 4 inches, a span is 9 inches)

12. GOLD : MALLEABLE :: CHALK : FRIABLE (rhyming pattern)

13. EASY JOB : SINECURE :: GUIDING LIGHT : CYNOSURE (the rhyming
pattern is the key here)

14. LEG : AMBULATE :: ARM : BRACHIATE

15. MOSQUITO : MALARIA :: CANNIBALISM : KURU (a disease limited to the
Fore tribe of New Guinea, who eat human brain in their religious
rituals)


16. HEAR : SEE :: TEMPORAL : OCCIPITAL (Lobes of the brain that deal
with hearing and sight.


17. ASTRONOMY AND PHYSICS : ASTROPHYSICS :: HISTORY AND STATISTICS :
CLIOMETRICS (Cliometrics is the use of statistics or economics in
historical studies.)


18. JEKYLL : HYDE :: ELOI : MORLOCKS (from the books by Robert Louis
Stevenson and H.G. Wells)

19. UNIVERSE : COSMO- :: UNIVERSAL LAWS : COSMONOMOLOGO-

20. SET OF SETS NOT MEMBERS OF THEMSELVES : RUSSELL :: DARKNESS OF THE
NIGHT SKY IN AN INFINITE UNIVERSE : OLBERS
(KEPLER has also been offered as an answer)

21. TEACHING : UPLIFTING :: PEDAGOGIC : ANAGOGIC (from Greek
for spiritual uplift)


22. LANGUAGE GAMES : LUDWIG :: PIANO CONCERTI FOR THE LEFT HAND : PAUL
(So obscure it is silly. Ludwig and Paul Wittgenstein were brothers.
One was a pianist, the other was the famous philosopher who used the
phrase "language games" in his book Philosophical Investigations.
Knowing this meaningless bit of trivia can hardly be an indication of
great intelligence.)


23. IDOLS : TWILIGHT :: MORALS : GENEALOGY (Titles of Nietzsche's
books)


24. SWEET*NESS* : SUFFIX :: BOAT*SWAIN* : STEM ("ness" is a suffix,
"swain" is the stem of the compound word "boatswain."
Alternate answer is BASE, which fits the rhyming pattern better


29. The answer is 20.


31. The answer is 22
(this answer may be wrong)

37.

Initially, we need to consider 11 possibilities where we choose 10
white marbles.
1) After the insertion, the box contains 10 whites. The chances of
this are 1 in 2^10, i.e. 1 in 1024. If this is the case, in our
subsequent drawing we're bound to pick out 10 whites. Total probability
of this possibility = 1/1024
2) After the insertion, the box contains 9 whites. The chances of this
are 10!/9!/1! = 10 in 1024. If this is the case, in our subsequent
drawing our chances of picking out 10 whites is (9/10)^10 because we
have a 9/10 chance each time. Total probability of this possibility =
10/1024 * (9/10)^10
3) After the insertion, the box contains 8 whites. The chances of this
are 10!/8!/2! = 45 in 1024. If this is the case, in our subsequent
drawing our chances of picking out 10 whites is (8/10)^10 because we
have a 8/10 chance each time. Total probability of this possibility =
45/1024 * (8/10)^10
4) Box = 7 whites. Total = 120/1024 * (7/10)^10 i.e. nCr * (r/10)^10
5) Box = 6 whites. Total = 210/1024 * (6/10)^10
6) Box = 5 whites. Total = 252/1024 * (5/10)^10
7) Box = 4 whites. Total = 210/1024 * (4/10)^10
8 ) Box = 3 whites. Total = 120/1024 * (3/10)^10
9) Box = 2 whites. Total = 45/1024 * (2/10)^10
10) Box = 1 whites. Total = 10/1024 * (1/10)^10
11) Box = 0 whites. Total = 1/1024 * (0/10)^10 = 0!!

So, the chances of drawing 10 whites is the sum of these which is
0.013913029625. Approximately. However, we know that we actually drew
10 whites, so this 1 in 72 (ish) chance has happened. The chance that
it happened because we had possibility 1) above is the chance of 1)
relative to this 0.0139... chance. So, the answer is
(1/1024)/0.013913029625 which is 0.070190499... i.e. 7%.
So there!

RESPONESE TO THIS ANSWER:

I suggest that the answer you have given is to the question "What is
the probability of you pulling out 10 white marbles one at a time?"
The question is, however, "what is the probability of all marbles being
white(or black)? The answer to that, I believe, is 1/1024, which to
nearest % is '0'.

REPLY TO RESPONSE:

I just re-read it, and I think I got it right. The question is, what is
the probability of them all being white, given that you randomly
withdrew and returned 10 white marbles consecutively.

38. 2 / 27

39. 8 / 3^7 or 4 / 3^27 (two solutions have been offered)

See an explanation here of 38 and 39 here:
http://groups.google.com/group/rec.puzzles/msg/8b1875e5406828ff?dmode=source

45. -4697

x = n^3 - n!

2^3 = 8, 2! = 2 so 8-2 = 6
3^3 = 27, 3! = 6 so 27-6 = 21
4^3 = 64, 4! = 24 so 64-24 = 40...


46. 95,041,567

the numbers are all products of increasingly large numbers of
successive primes.

2 = 2 (or 2x1?),
15 = 3x5,
1001 = 7x11x13,
215,441 = 17x19x23x29
and I think the next in the series should be
95,041,567 = 31x37x41x43x47.

47. 3 (The list is of the digits of pi/4)

48. pi^2 r^4 / 2 The hyper-volume of a 4-dimensional hyper-sphere.

[m***@aol.com]

Christ, not this can of worms again!

[b***@yahoo.com]

Good to see that my updates got posted. Let's try to work through the
quantitative section now.

Post by j***@yahoo.com
If you spot an error or would like to add answers, please reply to this
post or send me an e-mail, or both.
Don't forget to explain your answer, the more detail the better.
http://www.eskimo.com/~miyaguch/titan.html
1. STRIP : MoBIUS :: BOTTLE : KLEIN
2. THOUGHT : ACTION :: OBSESSIVE : COMPULSIVE
3. LACKING MONEY : PENURIOUS :: DOTING ON ONE'S WIFE : UXORIOUS
(definitions)
4. MICE : MEN :: CABBAGES : KINGS (from literature)
5. TIRE : RETREAD :: PARCHMENT : PALIMPSEST
6. ALL IS ONE : MONISM :: ALL IS SELF : SOLIPSISM (a doctrine in
philosophy, nothing exists except the self, or alternately the
existence of everything else depends on the existence of the self)
7. SWORD : DAMOCLES :: BED : PROCRUSTES
8. THING : DANGEROUS :: SPRING : PIERIAN
(A little learning is a dangerous thing; drink deep, or taste not the
Pierian spring - Alexander Pope. An
Essay on Criticism)
9. HOLLOW VICTORY : PYRRHIC :: HOLLOW VILLAGE : Potemkin
10. PILLAR : OBELISK :: MONSTER : BASILISK (OBELISK from Greek
obeliskos, BASILISK from Greek basiliskos)
11. 4 : HAND :: 9 : SPAN (a hand is 4 inches, a span is 9 inches)
12. GOLD : MALLEABLE :: CHALK : FRIABLE (rhyming pattern)
13. EASY JOB : SINECURE :: GUIDING LIGHT : CYNOSURE (the rhyming
pattern is the key here)
14. LEG : AMBULATE :: ARM : BRACHIATE
15. MOSQUITO : MALARIA :: CANNIBALISM : KURU (a disease limited to the
Fore tribe of New Guinea, who eat human brain in their religious
rituals)
16. HEAR : SEE :: TEMPORAL : OCCIPITAL (Lobes of the brain that deal
with hearing and sight.
CLIOMETRICS (Cliometrics is the use of statistics or economics in
historical studies.)
18. JEKYLL : HYDE :: ELOI : MORLOCKS (from the books by Robert Louis
Stevenson and H.G. Wells)
19. UNIVERSE : COSMO- :: UNIVERSAL LAWS : COSMONOMOLOGO-
20. SET OF SETS NOT MEMBERS OF THEMSELVES : RUSSELL :: DARKNESS OF THE
NIGHT SKY IN AN INFINITE UNIVERSE : OLBERS
(KEPLER has also been offered as an answer)
21. TEACHING : UPLIFTING :: PEDAGOGIC : ANAGOGIC (from Greek
for spiritual uplift)
22. LANGUAGE GAMES : LUDWIG :: PIANO CONCERTI FOR THE LEFT HAND : PAUL
(So obscure it is silly. Ludwig and Paul Wittgenstein were brothers.
One was a pianist, the other was the famous philosopher who used the
phrase "language games" in his book Philosophical Investigations.
Knowing this meaningless bit of trivia can hardly be an indication of
great intelligence.)
23. IDOLS : TWILIGHT :: MORALS : GENEALOGY (Titles of Nietzsche's
books)
24. SWEET*NESS* : SUFFIX :: BOAT*SWAIN* : STEM ("ness" is a suffix,
"swain" is the stem of the compound word "boatswain."
Alternate answer is BASE, which fits the rhyming pattern better
29. The answer is 20.
31. The answer is 22
(this answer may be wrong)
37.
Initially, we need to consider 11 possibilities where we choose 10
white marbles.
1) After the insertion, the box contains 10 whites. The chances of
this are 1 in 2^10, i.e. 1 in 1024. If this is the case, in our
subsequent drawing we're bound to pick out 10 whites. Total probability
of this possibility = 1/1024
2) After the insertion, the box contains 9 whites. The chances of this
are 10!/9!/1! = 10 in 1024. If this is the case, in our subsequent
drawing our chances of picking out 10 whites is (9/10)^10 because we
have a 9/10 chance each time. Total probability of this possibility =
10/1024 * (9/10)^10
3) After the insertion, the box contains 8 whites. The chances of this
are 10!/8!/2! = 45 in 1024. If this is the case, in our subsequent
drawing our chances of picking out 10 whites is (8/10)^10 because we
have a 8/10 chance each time. Total probability of this possibility =
45/1024 * (8/10)^10
4) Box = 7 whites. Total = 120/1024 * (7/10)^10 i.e. nCr * (r/10)^10
5) Box = 6 whites. Total = 210/1024 * (6/10)^10
6) Box = 5 whites. Total = 252/1024 * (5/10)^10
7) Box = 4 whites. Total = 210/1024 * (4/10)^10
8 ) Box = 3 whites. Total = 120/1024 * (3/10)^10
9) Box = 2 whites. Total = 45/1024 * (2/10)^10
10) Box = 1 whites. Total = 10/1024 * (1/10)^10
11) Box = 0 whites. Total = 1/1024 * (0/10)^10 = 0!!
So, the chances of drawing 10 whites is the sum of these which is
0.013913029625. Approximately. However, we know that we actually drew
10 whites, so this 1 in 72 (ish) chance has happened. The chance that
it happened because we had possibility 1) above is the chance of 1)
relative to this 0.0139... chance. So, the answer is
(1/1024)/0.013913029625 which is 0.070190499... i.e. 7%.
So there!
I suggest that the answer you have given is to the question "What is
the probability of you pulling out 10 white marbles one at a time?"
The question is, however, "what is the probability of all marbles being
white(or black)? The answer to that, I believe, is 1/1024, which to
nearest % is '0'.
I just re-read it, and I think I got it right. The question is, what is
the probability of them all being white, given that you randomly
withdrew and returned 10 white marbles consecutively.
38. 2 / 27
39. 8 / 3^7 or 4 / 3^27 (two solutions have been offered)
http://groups.google.com/group/rec.puzzles/msg/8b1875e5406828ff?dmode=source
45. -4697
x = n^3 - n!
2^3 = 8, 2! = 2 so 8-2 = 6
3^3 = 27, 3! = 6 so 27-6 = 21
4^3 = 64, 4! = 24 so 64-24 = 40...
46. 95,041,567
the numbers are all products of increasingly large numbers of
successive primes.
2 = 2 (or 2x1?),
15 = 3x5,
1001 = 7x11x13,
215,441 = 17x19x23x29
and I think the next in the series should be
95,041,567 = 31x37x41x43x47.
47. 3 (The list is of the digits of pi/4)
48. pi^2 r^4 / 2 The hyper-volume of a 4-dimensional hyper-sphere.

[b***@yahoo.com]

Unfortunately, judgerobertbork didn't include all of my qualifications
to the answers I provided on the verbal questions. I'll add them in the
near future.

For questions 25-48:

25. 9
26. 11
27. 14
28. 21
29. 26
30. 7
31. 32
32. 48
33. 12 or 13
34. 49
35. ?
36. 9
37. 7%
38. 2/27
39. 8/2187
40. 3/256
41. 4/129140163
42. 1856/48828135
43. 25
44. 2530
45. -4697
46. 95041567
47. 3
48. p2r4 / 2

I will provide detailed explanations for each of the above in
additional posts.

Post by j***@yahoo.com
If you spot an error or would like to add answers, please reply to this
post or send me an e-mail, or both.
Don't forget to explain your answer, the more detail the better.
http://www.eskimo.com/~miyaguch/titan.html
1. STRIP : MoBIUS :: BOTTLE : KLEIN
2. THOUGHT : ACTION :: OBSESSIVE : COMPULSIVE
3. LACKING MONEY : PENURIOUS :: DOTING ON ONE'S WIFE : UXORIOUS
(definitions)
4. MICE : MEN :: CABBAGES : KINGS (from literature)
5. TIRE : RETREAD :: PARCHMENT : PALIMPSEST
6. ALL IS ONE : MONISM :: ALL IS SELF : SOLIPSISM (a doctrine in
philosophy, nothing exists except the self, or alternately the
existence of everything else depends on the existence of the self)
7. SWORD : DAMOCLES :: BED : PROCRUSTES
8. THING : DANGEROUS :: SPRING : PIERIAN
(A little learning is a dangerous thing; drink deep, or taste not the
Pierian spring - Alexander Pope. An
Essay on Criticism)
9. HOLLOW VICTORY : PYRRHIC :: HOLLOW VILLAGE : Potemkin
10. PILLAR : OBELISK :: MONSTER : BASILISK (OBELISK from Greek
obeliskos, BASILISK from Greek basiliskos)
11. 4 : HAND :: 9 : SPAN (a hand is 4 inches, a span is 9 inches)
12. GOLD : MALLEABLE :: CHALK : FRIABLE (rhyming pattern)
13. EASY JOB : SINECURE :: GUIDING LIGHT : CYNOSURE (the rhyming
pattern is the key here)
14. LEG : AMBULATE :: ARM : BRACHIATE
15. MOSQUITO : MALARIA :: CANNIBALISM : KURU (a disease limited to the
Fore tribe of New Guinea, who eat human brain in their religious
rituals)
16. HEAR : SEE :: TEMPORAL : OCCIPITAL (Lobes of the brain that deal
with hearing and sight.
CLIOMETRICS (Cliometrics is the use of statistics or economics in
historical studies.)
18. JEKYLL : HYDE :: ELOI : MORLOCKS (from the books by Robert Louis
Stevenson and H.G. Wells)
19. UNIVERSE : COSMO- :: UNIVERSAL LAWS : COSMONOMOLOGO-
20. SET OF SETS NOT MEMBERS OF THEMSELVES : RUSSELL :: DARKNESS OF THE
NIGHT SKY IN AN INFINITE UNIVERSE : OLBERS
(KEPLER has also been offered as an answer)
21. TEACHING : UPLIFTING :: PEDAGOGIC : ANAGOGIC (from Greek
for spiritual uplift)
22. LANGUAGE GAMES : LUDWIG :: PIANO CONCERTI FOR THE LEFT HAND : PAUL
(So obscure it is silly. Ludwig and Paul Wittgenstein were brothers.
One was a pianist, the other was the famous philosopher who used the
phrase "language games" in his book Philosophical Investigations.
Knowing this meaningless bit of trivia can hardly be an indication of
great intelligence.)
23. IDOLS : TWILIGHT :: MORALS : GENEALOGY (Titles of Nietzsche's
books)
24. SWEET*NESS* : SUFFIX :: BOAT*SWAIN* : STEM ("ness" is a suffix,
"swain" is the stem of the compound word "boatswain."
Alternate answer is BASE, which fits the rhyming pattern better
29. The answer is 20.
31. The answer is 22
(this answer may be wrong)
37.
Initially, we need to consider 11 possibilities where we choose 10
white marbles.
1) After the insertion, the box contains 10 whites. The chances of
this are 1 in 2^10, i.e. 1 in 1024. If this is the case, in our
subsequent drawing we're bound to pick out 10 whites. Total probability
of this possibility = 1/1024
2) After the insertion, the box contains 9 whites. The chances of this
are 10!/9!/1! = 10 in 1024. If this is the case, in our subsequent
drawing our chances of picking out 10 whites is (9/10)^10 because we
have a 9/10 chance each time. Total probability of this possibility =
10/1024 * (9/10)^10
3) After the insertion, the box contains 8 whites. The chances of this
are 10!/8!/2! = 45 in 1024. If this is the case, in our subsequent
drawing our chances of picking out 10 whites is (8/10)^10 because we
have a 8/10 chance each time. Total probability of this possibility =
45/1024 * (8/10)^10
4) Box = 7 whites. Total = 120/1024 * (7/10)^10 i.e. nCr * (r/10)^10
5) Box = 6 whites. Total = 210/1024 * (6/10)^10
6) Box = 5 whites. Total = 252/1024 * (5/10)^10
7) Box = 4 whites. Total = 210/1024 * (4/10)^10
8 ) Box = 3 whites. Total = 120/1024 * (3/10)^10
9) Box = 2 whites. Total = 45/1024 * (2/10)^10
10) Box = 1 whites. Total = 10/1024 * (1/10)^10
11) Box = 0 whites. Total = 1/1024 * (0/10)^10 = 0!!
So, the chances of drawing 10 whites is the sum of these which is
0.013913029625. Approximately. However, we know that we actually drew
10 whites, so this 1 in 72 (ish) chance has happened. The chance that
it happened because we had possibility 1) above is the chance of 1)
relative to this 0.0139... chance. So, the answer is
(1/1024)/0.013913029625 which is 0.070190499... i.e. 7%.
So there!
I suggest that the answer you have given is to the question "What is
the probability of you pulling out 10 white marbles one at a time?"
The question is, however, "what is the probability of all marbles being
white(or black)? The answer to that, I believe, is 1/1024, which to
nearest % is '0'.
I just re-read it, and I think I got it right. The question is, what is
the probability of them all being white, given that you randomly
withdrew and returned 10 white marbles consecutively.
38. 2 / 27
39. 8 / 3^7 or 4 / 3^27 (two solutions have been offered)
http://groups.google.com/group/rec.puzzles/msg/8b1875e5406828ff?dmode=source
45. -4697
x = n^3 - n!
2^3 = 8, 2! = 2 so 8-2 = 6
3^3 = 27, 3! = 6 so 27-6 = 21
4^3 = 64, 4! = 24 so 64-24 = 40...
46. 95,041,567
the numbers are all products of increasingly large numbers of
successive primes.
2 = 2 (or 2x1?),
15 = 3x5,
1001 = 7x11x13,
215,441 = 17x19x23x29
and I think the next in the series should be
95,041,567 = 31x37x41x43x47.
47. 3 (The list is of the digits of pi/4)
48. pi^2 r^4 / 2 The hyper-volume of a 4-dimensional hyper-sphere.

[b***@yahoo.com]

Question 26. This question can be solved with no more than 11 squares.
The approach is similar to that taken in solving question 25 in the
previous post. For simplicity, let's first assume that we are
building a square with sides of 5" in length. Next, let's divide
the interior into 25 imaginary inner 1" x 1" square spaces that we
will number from 1 to 25 going from left to right and top to bottom. In
other words:

1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
16 17 18 19 20
21 22 23 24 25

Step 1. Lay down a 5" x 5" square as the base.

Step 2. Lay down 1" x 1" squares over spaces 3, 11, 13, 15, 17, and
23.

Step 3. Lay down 1.41" x 1.41" squares (i.e. square root of 2 x
square root of 2, with 2" diagonals) in diamond configurations
directly over spaces 1, 2, 6, and 7 and spaces 19, 20, 24 and 25,
respectively.

Step 4. Lay down a 2" x 2" square over spaces 4, 5, 9 and 10.

Step 5. Lay down a 1" x 1" square over space 10.

Post by j***@yahoo.com
If you spot an error or would like to add answers, please reply to this
post or send me an e-mail, or both.
Don't forget to explain your answer, the more detail the better.
http://www.eskimo.com/~miyaguch/titan.html
1. STRIP : MoBIUS :: BOTTLE : KLEIN
2. THOUGHT : ACTION :: OBSESSIVE : COMPULSIVE
3. LACKING MONEY : PENURIOUS :: DOTING ON ONE'S WIFE : UXORIOUS
(definitions)
4. MICE : MEN :: CABBAGES : KINGS (from literature)
5. TIRE : RETREAD :: PARCHMENT : PALIMPSEST
6. ALL IS ONE : MONISM :: ALL IS SELF : SOLIPSISM (a doctrine in
philosophy, nothing exists except the self, or alternately the
existence of everything else depends on the existence of the self)
7. SWORD : DAMOCLES :: BED : PROCRUSTES
8. THING : DANGEROUS :: SPRING : PIERIAN
(A little learning is a dangerous thing; drink deep, or taste not the
Pierian spring - Alexander Pope. An
Essay on Criticism)
9. HOLLOW VICTORY : PYRRHIC :: HOLLOW VILLAGE : Potemkin
10. PILLAR : OBELISK :: MONSTER : BASILISK (OBELISK from Greek
obeliskos, BASILISK from Greek basiliskos)
11. 4 : HAND :: 9 : SPAN (a hand is 4 inches, a span is 9 inches)
12. GOLD : MALLEABLE :: CHALK : FRIABLE (rhyming pattern)
13. EASY JOB : SINECURE :: GUIDING LIGHT : CYNOSURE (the rhyming
pattern is the key here)
14. LEG : AMBULATE :: ARM : BRACHIATE
15. MOSQUITO : MALARIA :: CANNIBALISM : KURU (a disease limited to the
Fore tribe of New Guinea, who eat human brain in their religious
rituals)
16. HEAR : SEE :: TEMPORAL : OCCIPITAL (Lobes of the brain that deal
with hearing and sight.
CLIOMETRICS (Cliometrics is the use of statistics or economics in
historical studies.)
18. JEKYLL : HYDE :: ELOI : MORLOCKS (from the books by Robert Louis
Stevenson and H.G. Wells)
19. UNIVERSE : COSMO- :: UNIVERSAL LAWS : COSMONOMOLOGO-
20. SET OF SETS NOT MEMBERS OF THEMSELVES : RUSSELL :: DARKNESS OF THE
NIGHT SKY IN AN INFINITE UNIVERSE : OLBERS
(KEPLER has also been offered as an answer)
21. TEACHING : UPLIFTING :: PEDAGOGIC : ANAGOGIC (from Greek
for spiritual uplift)
22. LANGUAGE GAMES : LUDWIG :: PIANO CONCERTI FOR THE LEFT HAND : PAUL
(So obscure it is silly. Ludwig and Paul Wittgenstein were brothers.
One was a pianist, the other was the famous philosopher who used the
phrase "language games" in his book Philosophical Investigations.
Knowing this meaningless bit of trivia can hardly be an indication of
great intelligence.)
23. IDOLS : TWILIGHT :: MORALS : GENEALOGY (Titles of Nietzsche's
books)
24. SWEET*NESS* : SUFFIX :: BOAT*SWAIN* : STEM ("ness" is a suffix,
"swain" is the stem of the compound word "boatswain."
Alternate answer is BASE, which fits the rhyming pattern better
29. The answer is 20.
31. The answer is 22
(this answer may be wrong)
37.
Initially, we need to consider 11 possibilities where we choose 10
white marbles.
1) After the insertion, the box contains 10 whites. The chances of
this are 1 in 2^10, i.e. 1 in 1024. If this is the case, in our
subsequent drawing we're bound to pick out 10 whites. Total probability
of this possibility = 1/1024
2) After the insertion, the box contains 9 whites. The chances of this
are 10!/9!/1! = 10 in 1024. If this is the case, in our subsequent
drawing our chances of picking out 10 whites is (9/10)^10 because we
have a 9/10 chance each time. Total probability of this possibility =
10/1024 * (9/10)^10
3) After the insertion, the box contains 8 whites. The chances of this
are 10!/8!/2! = 45 in 1024. If this is the case, in our subsequent
drawing our chances of picking out 10 whites is (8/10)^10 because we
have a 8/10 chance each time. Total probability of this possibility =
45/1024 * (8/10)^10
4) Box = 7 whites. Total = 120/1024 * (7/10)^10 i.e. nCr * (r/10)^10
5) Box = 6 whites. Total = 210/1024 * (6/10)^10
6) Box = 5 whites. Total = 252/1024 * (5/10)^10
7) Box = 4 whites. Total = 210/1024 * (4/10)^10
8 ) Box = 3 whites. Total = 120/1024 * (3/10)^10
9) Box = 2 whites. Total = 45/1024 * (2/10)^10
10) Box = 1 whites. Total = 10/1024 * (1/10)^10
11) Box = 0 whites. Total = 1/1024 * (0/10)^10 = 0!!
So, the chances of drawing 10 whites is the sum of these which is
0.013913029625. Approximately. However, we know that we actually drew
10 whites, so this 1 in 72 (ish) chance has happened. The chance that
it happened because we had possibility 1) above is the chance of 1)
relative to this 0.0139... chance. So, the answer is
(1/1024)/0.013913029625 which is 0.070190499... i.e. 7%.
So there!
I suggest that the answer you have given is to the question "What is
the probability of you pulling out 10 white marbles one at a time?"
The question is, however, "what is the probability of all marbles being
white(or black)? The answer to that, I believe, is 1/1024, which to
nearest % is '0'.
I just re-read it, and I think I got it right. The question is, what is
the probability of them all being white, given that you randomly
withdrew and returned 10 white marbles consecutively.
38. 2 / 27
39. 8 / 3^7 or 4 / 3^27 (two solutions have been offered)
http://groups.google.com/group/rec.puzzles/msg/8b1875e5406828ff?dmode=source
45. -4697
x = n^3 - n!
2^3 = 8, 2! = 2 so 8-2 = 6
3^3 = 27, 3! = 6 so 27-6 = 21
4^3 = 64, 4! = 24 so 64-24 = 40...
46. 95,041,567
the numbers are all products of increasingly large numbers of
successive primes.
2 = 2 (or 2x1?),
15 = 3x5,
1001 = 7x11x13,
215,441 = 17x19x23x29
and I think the next in the series should be
95,041,567 = 31x37x41x43x47.
47. 3 (The list is of the digits of pi/4)
48. pi^2 r^4 / 2 The hyper-volume of a 4-dimensional hyper-sphere.

[b***@yahoo.com]

Evidently, my answer to Question 25 disappeared in cyberspace. Hence,
I'll repost.

Question 25. This can be solved with nine squares. For simplicity,
let's first assume that we are building a square with sides of 4"
in length. Next, let's divide the interior into 16 imaginary inner
1" x 1" square spaces that we will number from 1 to 16 going from
left to right and top to bottom. In other words:

1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16

Step 1. Lay down a 4" x 4" square as the base.

Step 2. Lay down a 3" x 3" square on top of the base on the lower
right side (covering
spaces 6 ,7, 8, 10, 11, 12, 14, 15, 16).

Step 3. Lay down a 2" x 2" square on top of the 3" x 3" square
on the lower right side (covering spaces 11, 12, 15, 16).

Step 4. Lay down a 2" x 2" square in the top middle of the 4" x
4" square (covering spaces 2, 3, 6 and 7).

Step 5. Lay down a 1" x 1" square over space 11.

Step 6. Lay down a 1" x 1" square over space 3.

Step 7. Lay down a 1" x 1" square over space 5.

Step 8. Lay down a 1" x 1" square over space 13.

Step 9. Lay down a 1.41" x 1.41" square (i.e. square root of 2 x
square root of 2, which has 2" diagonals) in a diamond configuration
directly in the middle of the 4" x 4" base.

If you want to try to solve this yourself visually, try using cardboard
pieces of different sizes and colors.

Post by j***@yahoo.com
If you spot an error or would like to add answers, please reply to this
post or send me an e-mail, or both.
Don't forget to explain your answer, the more detail the better.
http://www.eskimo.com/~miyaguch/titan.html
1. STRIP : MoBIUS :: BOTTLE : KLEIN
2. THOUGHT : ACTION :: OBSESSIVE : COMPULSIVE
3. LACKING MONEY : PENURIOUS :: DOTING ON ONE'S WIFE : UXORIOUS
(definitions)
4. MICE : MEN :: CABBAGES : KINGS (from literature)
5. TIRE : RETREAD :: PARCHMENT : PALIMPSEST
6. ALL IS ONE : MONISM :: ALL IS SELF : SOLIPSISM (a doctrine in
philosophy, nothing exists except the self, or alternately the
existence of everything else depends on the existence of the self)
7. SWORD : DAMOCLES :: BED : PROCRUSTES
8. THING : DANGEROUS :: SPRING : PIERIAN
(A little learning is a dangerous thing; drink deep, or taste not the
Pierian spring - Alexander Pope. An
Essay on Criticism)
9. HOLLOW VICTORY : PYRRHIC :: HOLLOW VILLAGE : Potemkin
10. PILLAR : OBELISK :: MONSTER : BASILISK (OBELISK from Greek
obeliskos, BASILISK from Greek basiliskos)
11. 4 : HAND :: 9 : SPAN (a hand is 4 inches, a span is 9 inches)
12. GOLD : MALLEABLE :: CHALK : FRIABLE (rhyming pattern)
13. EASY JOB : SINECURE :: GUIDING LIGHT : CYNOSURE (the rhyming
pattern is the key here)
14. LEG : AMBULATE :: ARM : BRACHIATE
15. MOSQUITO : MALARIA :: CANNIBALISM : KURU (a disease limited to the
Fore tribe of New Guinea, who eat human brain in their religious
rituals)
16. HEAR : SEE :: TEMPORAL : OCCIPITAL (Lobes of the brain that deal
with hearing and sight.
CLIOMETRICS (Cliometrics is the use of statistics or economics in
historical studies.)
18. JEKYLL : HYDE :: ELOI : MORLOCKS (from the books by Robert Louis
Stevenson and H.G. Wells)
19. UNIVERSE : COSMO- :: UNIVERSAL LAWS : COSMONOMOLOGO-
20. SET OF SETS NOT MEMBERS OF THEMSELVES : RUSSELL :: DARKNESS OF THE
NIGHT SKY IN AN INFINITE UNIVERSE : OLBERS
(KEPLER has also been offered as an answer)
21. TEACHING : UPLIFTING :: PEDAGOGIC : ANAGOGIC (from Greek
for spiritual uplift)
22. LANGUAGE GAMES : LUDWIG :: PIANO CONCERTI FOR THE LEFT HAND : PAUL
(So obscure it is silly. Ludwig and Paul Wittgenstein were brothers.
One was a pianist, the other was the famous philosopher who used the
phrase "language games" in his book Philosophical Investigations.
Knowing this meaningless bit of trivia can hardly be an indication of
great intelligence.)
23. IDOLS : TWILIGHT :: MORALS : GENEALOGY (Titles of Nietzsche's
books)
24. SWEET*NESS* : SUFFIX :: BOAT*SWAIN* : STEM ("ness" is a suffix,
"swain" is the stem of the compound word "boatswain."
Alternate answer is BASE, which fits the rhyming pattern better
29. The answer is 20.
31. The answer is 22
(this answer may be wrong)
37.
Initially, we need to consider 11 possibilities where we choose 10
white marbles.
1) After the insertion, the box contains 10 whites. The chances of
this are 1 in 2^10, i.e. 1 in 1024. If this is the case, in our
subsequent drawing we're bound to pick out 10 whites. Total probability
of this possibility = 1/1024
2) After the insertion, the box contains 9 whites. The chances of this
are 10!/9!/1! = 10 in 1024. If this is the case, in our subsequent
drawing our chances of picking out 10 whites is (9/10)^10 because we
have a 9/10 chance each time. Total probability of this possibility =
10/1024 * (9/10)^10
3) After the insertion, the box contains 8 whites. The chances of this
are 10!/8!/2! = 45 in 1024. If this is the case, in our subsequent
drawing our chances of picking out 10 whites is (8/10)^10 because we
have a 8/10 chance each time. Total probability of this possibility =
45/1024 * (8/10)^10
4) Box = 7 whites. Total = 120/1024 * (7/10)^10 i.e. nCr * (r/10)^10
5) Box = 6 whites. Total = 210/1024 * (6/10)^10
6) Box = 5 whites. Total = 252/1024 * (5/10)^10
7) Box = 4 whites. Total = 210/1024 * (4/10)^10
8 ) Box = 3 whites. Total = 120/1024 * (3/10)^10
9) Box = 2 whites. Total = 45/1024 * (2/10)^10
10) Box = 1 whites. Total = 10/1024 * (1/10)^10
11) Box = 0 whites. Total = 1/1024 * (0/10)^10 = 0!!
So, the chances of drawing 10 whites is the sum of these which is
0.013913029625. Approximately. However, we know that we actually drew
10 whites, so this 1 in 72 (ish) chance has happened. The chance that
it happened because we had possibility 1) above is the chance of 1)
relative to this 0.0139... chance. So, the answer is
(1/1024)/0.013913029625 which is 0.070190499... i.e. 7%.
So there!
I suggest that the answer you have given is to the question "What is
the probability of you pulling out 10 white marbles one at a time?"
The question is, however, "what is the probability of all marbles being
white(or black)? The answer to that, I believe, is 1/1024, which to
nearest % is '0'.
I just re-read it, and I think I got it right. The question is, what is
the probability of them all being white, given that you randomly
withdrew and returned 10 white marbles consecutively.
38. 2 / 27
39. 8 / 3^7 or 4 / 3^27 (two solutions have been offered)
http://groups.google.com/group/rec.puzzles/msg/8b1875e5406828ff?dmode=source
45. -4697
x = n^3 - n!
2^3 = 8, 2! = 2 so 8-2 = 6
3^3 = 27, 3! = 6 so 27-6 = 21
4^3 = 64, 4! = 24 so 64-24 = 40...
46. 95,041,567
the numbers are all products of increasingly large numbers of
successive primes.
2 = 2 (or 2x1?),
15 = 3x5,
1001 = 7x11x13,
215,441 = 17x19x23x29
and I think the next in the series should be
95,041,567 = 31x37x41x43x47.
47. 3 (The list is of the digits of pi/4)
48. pi^2 r^4 / 2 The hyper-volume of a 4-dimensional hyper-sphere.

[b***@yahoo.com]

Question 25. This can be solved with no more than nine squares of
various sizes, lying one on top of another. For simplicity, let's
first assume that we are building a square with sides of 4" in
length. Next, let's divide the interior into 16 imaginary inner 1"
x 1" square spaces that we will number from 1 to 16 going from left
to right and top to bottom. In other words:

1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16

Step 1. Lay down a 4" x 4" square as the base.

Step 2. Lay down a 3" x 3" square on top of the base on the lower
right side (covering spaces 6 ,7, 8, 10, 11, 12, 14, 15, 16).

Step 3. Lay down a 2" x 2" square on top of the 3" x 3" square
on the lower right side (covering spaces 11, 12, 15, 16).

Step 4. Lay down a 2" x 2" square in the top middle of the 4" x
4" square (covering spaces 2, 3, 6 and 7).

Step 5. Lay down a 1" x 1" square over space 11.

Step 6. Lay down a 1" x 1" square over space 3.

Step 7. Lay down a 1" x 1" square over space 5.

Step 8. Lay down a 1" x 1" square over space 13.

Step 9. Lay down a 1.41" x 1.41" square (i.e. square root of 2 x
square root of 2, which has 2" diagonals) in a diamond configuration
directly in the middle of the 4" x 4" base.

If you want to try to solve this yourself visually, try using cardboard
pieces of different sizes and colors.

Post by j***@yahoo.com
If you spot an error or would like to add answers, please reply to this
post or send me an e-mail, or both.
Don't forget to explain your answer, the more detail the better.
http://www.eskimo.com/~miyaguch/titan.html
1. STRIP : MoBIUS :: BOTTLE : KLEIN
2. THOUGHT : ACTION :: OBSESSIVE : COMPULSIVE
3. LACKING MONEY : PENURIOUS :: DOTING ON ONE'S WIFE : UXORIOUS
(definitions)
4. MICE : MEN :: CABBAGES : KINGS (from literature)
5. TIRE : RETREAD :: PARCHMENT : PALIMPSEST
6. ALL IS ONE : MONISM :: ALL IS SELF : SOLIPSISM (a doctrine in
philosophy, nothing exists except the self, or alternately the
existence of everything else depends on the existence of the self)
7. SWORD : DAMOCLES :: BED : PROCRUSTES
8. THING : DANGEROUS :: SPRING : PIERIAN
(A little learning is a dangerous thing; drink deep, or taste not the
Pierian spring - Alexander Pope. An
Essay on Criticism)
9. HOLLOW VICTORY : PYRRHIC :: HOLLOW VILLAGE : Potemkin
10. PILLAR : OBELISK :: MONSTER : BASILISK (OBELISK from Greek
obeliskos, BASILISK from Greek basiliskos)
11. 4 : HAND :: 9 : SPAN (a hand is 4 inches, a span is 9 inches)
12. GOLD : MALLEABLE :: CHALK : FRIABLE (rhyming pattern)
13. EASY JOB : SINECURE :: GUIDING LIGHT : CYNOSURE (the rhyming
pattern is the key here)
14. LEG : AMBULATE :: ARM : BRACHIATE
15. MOSQUITO : MALARIA :: CANNIBALISM : KURU (a disease limited to the
Fore tribe of New Guinea, who eat human brain in their religious
rituals)
16. HEAR : SEE :: TEMPORAL : OCCIPITAL (Lobes of the brain that deal
with hearing and sight.
CLIOMETRICS (Cliometrics is the use of statistics or economics in
historical studies.)
18. JEKYLL : HYDE :: ELOI : MORLOCKS (from the books by Robert Louis
Stevenson and H.G. Wells)
19. UNIVERSE : COSMO- :: UNIVERSAL LAWS : COSMONOMOLOGO-
20. SET OF SETS NOT MEMBERS OF THEMSELVES : RUSSELL :: DARKNESS OF THE
NIGHT SKY IN AN INFINITE UNIVERSE : OLBERS
(KEPLER has also been offered as an answer)
21. TEACHING : UPLIFTING :: PEDAGOGIC : ANAGOGIC (from Greek
for spiritual uplift)
22. LANGUAGE GAMES : LUDWIG :: PIANO CONCERTI FOR THE LEFT HAND : PAUL
(So obscure it is silly. Ludwig and Paul Wittgenstein were brothers.
One was a pianist, the other was the famous philosopher who used the
phrase "language games" in his book Philosophical Investigations.
Knowing this meaningless bit of trivia can hardly be an indication of
great intelligence.)
23. IDOLS : TWILIGHT :: MORALS : GENEALOGY (Titles of Nietzsche's
books)
24. SWEET*NESS* : SUFFIX :: BOAT*SWAIN* : STEM ("ness" is a suffix,
"swain" is the stem of the compound word "boatswain."
Alternate answer is BASE, which fits the rhyming pattern better
29. The answer is 20.
31. The answer is 22
(this answer may be wrong)
37.
Initially, we need to consider 11 possibilities where we choose 10
white marbles.
1) After the insertion, the box contains 10 whites. The chances of
this are 1 in 2^10, i.e. 1 in 1024. If this is the case, in our
subsequent drawing we're bound to pick out 10 whites. Total probability
of this possibility = 1/1024
2) After the insertion, the box contains 9 whites. The chances of this
are 10!/9!/1! = 10 in 1024. If this is the case, in our subsequent
drawing our chances of picking out 10 whites is (9/10)^10 because we
have a 9/10 chance each time. Total probability of this possibility =
10/1024 * (9/10)^10
3) After the insertion, the box contains 8 whites. The chances of this
are 10!/8!/2! = 45 in 1024. If this is the case, in our subsequent
drawing our chances of picking out 10 whites is (8/10)^10 because we
have a 8/10 chance each time. Total probability of this possibility =
45/1024 * (8/10)^10
4) Box = 7 whites. Total = 120/1024 * (7/10)^10 i.e. nCr * (r/10)^10
5) Box = 6 whites. Total = 210/1024 * (6/10)^10
6) Box = 5 whites. Total = 252/1024 * (5/10)^10
7) Box = 4 whites. Total = 210/1024 * (4/10)^10
8 ) Box = 3 whites. Total = 120/1024 * (3/10)^10
9) Box = 2 whites. Total = 45/1024 * (2/10)^10
10) Box = 1 whites. Total = 10/1024 * (1/10)^10
11) Box = 0 whites. Total = 1/1024 * (0/10)^10 = 0!!
So, the chances of drawing 10 whites is the sum of these which is
0.013913029625. Approximately. However, we know that we actually drew
10 whites, so this 1 in 72 (ish) chance has happened. The chance that
it happened because we had possibility 1) above is the chance of 1)
relative to this 0.0139... chance. So, the answer is
(1/1024)/0.013913029625 which is 0.070190499... i.e. 7%.
So there!
I suggest that the answer you have given is to the question "What is
the probability of you pulling out 10 white marbles one at a time?"
The question is, however, "what is the probability of all marbles being
white(or black)? The answer to that, I believe, is 1/1024, which to
nearest % is '0'.
I just re-read it, and I think I got it right. The question is, what is
the probability of them all being white, given that you randomly
withdrew and returned 10 white marbles consecutively.
38. 2 / 27
39. 8 / 3^7 or 4 / 3^27 (two solutions have been offered)
http://groups.google.com/group/rec.puzzles/msg/8b1875e5406828ff?dmode=source
45. -4697
x = n^3 - n!
2^3 = 8, 2! = 2 so 8-2 = 6
3^3 = 27, 3! = 6 so 27-6 = 21
4^3 = 64, 4! = 24 so 64-24 = 40...
46. 95,041,567
the numbers are all products of increasingly large numbers of
successive primes.
2 = 2 (or 2x1?),
15 = 3x5,
1001 = 7x11x13,
215,441 = 17x19x23x29
and I think the next in the series should be
95,041,567 = 31x37x41x43x47.
47. 3 (The list is of the digits of pi/4)
48. pi^2 r^4 / 2 The hyper-volume of a 4-dimensional hyper-sphere.

[b***@yahoo.com]

Question 30. This question can be answered using 2-D representation or
3-D. For the purposes of this use group, we'll have to use the 2-D
approach, which simply involves drawing a schematic diagram
representing the six sides of a cube and determining the unique
combinations of diagonals. Based on the rather crude schematic below,
each side of the cube is numbered from 1 to 6 going from top to bottom
and left to right.
_____
| 1 |
| ____ |
| 2 |
____ | ____ | ____
| 3 | 4 | 5 |
|____ | ____ |____ |
| 6 |
| ____ |

[note, this schematic does not appear correctly when posted, but the
relative position of the numbers is correct.]


Each unique combination can then be represented by a six-square grid
like the one above, with each square containing either of two possible
diagonals, represented by a forward slash and a backward slash,
respectively.

Combination 1:
Sq 1: /
Sq 2: \
Sq 3: \
Sq 4: \
Sq 5: /
Sq 6: /
Combination 2:
Sq 1: /
Sq 2: \
Sq 3: /
Sq 4: /
Sq 5: /
Sq 6: \
Combination 3:
Sq 1: /
Sq 2: /
Sq 3: \
Sq 4: /
Sq 5: \
Sq 6: \
Combination 4:
Sq 1: /
Sq 2: \
Sq 3: \
Sq 4: /
Sq 5: \
Sq 6: \
Combination 5:
Sq 1: \
Sq 2: \
Sq 3: \
Sq 4: \
Sq 5: \
Sq 6: /
Combination 6:
Sq 1: /
Sq 2: /
Sq 3: \
Sq 4: \
Sq 5: \
Sq 6: /
Combination 6:
Sq 1: /
Sq 2: /
Sq 3: /
Sq 4: /
Sq 5: \
Sq 6: \


Because it is hard to visualize these combinations in two dimensions,
to really understand the answer to this problem it is best to use a set
of small plastic blocks (e.g., 2" x 2"). These can be purchased in
the toy section of a department store. Cut a small square piece of
masking tape and place it on each of the six sides of each plastic
block (according to my calculations, you only need 7 blocks). Number
each piece of tape from 1 to 6. Then mark each piece of tape with the
various diagonals. After you have done that, take one block in each
hand and see if you can superimpose one on the other (totally ignore
the numbers when you're doing this). If not, then the two blocks are
unique. Then take a third block and see if you can superimpose it on
the first two. If not, then all three blocks are unique. Keep doing
this until you have 7 unique blocks.

[b***@yahoo.com]

Titan Question 29. To solve this problem, let's look at the cube
from a frontal perspective, which corresponds to the graphic shown on
the Titan Test. Each of the 27 cubes will be represented by the numbers
1 to 27. The nine cubes in the front layer are numbered from 1 to 9
going from left to right and top to bottom. The nine cubes in the
middle layer are numbered from 10 to 18 going from left to right and
top to bottom. The nine cubes in the rear layer are numbered from 19 to
27 going from left to right and top to bottom. Using this nomenclature,
each unique combination of two missing cubes can be represented by two
numbers.

1. 1 + 2
2. 1 + 3
3. 1 + 5
4. 1 + 6
5. 1 + 8
6. 1 + 9
7. 1 + 14
8. 1 + 15
9. 1 + 18
10. 1 + 24
11. 1 + 26
12. 1 + 27
13. 2 + 4
14. 2 + 5
15. 2 + 8
16. 2 + 13
17. 2 + 14
18. 2 + 16
19. 2 + 17
20. 2 + 18
21. 2 + 23
22. 2 + 26
23. 5 + 11
24. 5 + 14
25. 5 + 23

Hmm. I originally got 26, but it looks like 25 now that I've worked it
out more methodically.

[b***@yahoo.com]

Question 28. To solve this problem, let's look at the octahedron from
a frontal perspective that shows four sides of the octahedron, with
each side corresponding to equilateral triangles which will be
designated 1, 2, 3 and 4, respectively, going from left to right and
top to bottom. The four corresponding back sides of the octahedron will
be designated 5, 6, 7 and 8 going from left to right and top to bottom.
There are at least 19 possibilities:

1. All sides black
2. Any one side black
3. Sides 1 + 2 black (sides adjacent)
4. Sides 1 + 4 black (vertices adjacent)
5. Sides 1 + 8 black (sides opposite)
6. Sides 1, 2 and 3 black (sides adjacent)
7. Sides 1, 2 and 7 black
8. Sides 1, 2, 3 and 4 black
9. Sides 1, 2, 3 and 8 black
10. Sides 1, 2, 7 and 8 black
11. All sides white
12. Any one side white
13. Sides 1 + 2 white
14. Sides 1 + 4 white
15. Sides 1 + 8 white
16. Sides 1, 2 and 3 white
17. Sides 1, 2 and 7 white
18. Sides 1, 2, 3 and 4 white
19. Sides 1, 2, 3 and 8 white

Okay. I originally got 21 possibilities doing it in my head. Now it
looks like 19.

[j***@yahoo.com]

Thanks for the answers Blue Monday, keep 'em coming.

[b***@yahoo.com]

Post by j***@yahoo.com
Thanks for the answers Blue Monday, keep 'em coming.

Okay, let's wrap up the spatial problems subsection of the test.

Question 27. I seem to recall solving this problem with 14 squares at
one time, but I did it my head then without systematically working
through it on paper. This question can definitely be solved with no
more than 15 squares. For simplicity, let's assume that we are
building a square with sides of 6" in length. Next, let's divide
the interior into 36 imaginary inner 1" x 1" square spaces that are
numbered from 1 to 36 going from left to right and top to bottom. In
other words:

1 2 3 4 5 6
7 8 9 10 11 12
13 14 15 16 17 18
19 20 21 22 23 24
25 26 27 28 29 30
31 32 33 34 35 36


Step 1. Lay down a 6" x 6" square as the base

Step 2. Lay down a 5" x 5" square over spaces 2-6, 8-12, 14-18,
20-24 and 26-30

Step 3. Lay down a 5" x 5" square over spaces 8-12, 14-18, 20-24,
26-30 and 32-36

Step 4. Lay down a 4" x 4" square over spaces 8-11, 14-17, 20-23
and 26-29

Step 5. Lay down a 3" x 3" square over spaces 4-6, 10-12 and 16-18

Step 6. Lay down a 2" x 2" square over spaces 4, 5, 10 and 11

Step 7. Lay down a 3" x 3" square over spaces 15-17, 21-23 and
27-29

Step 8. Lay down a 1" x 1" square over space 11

Step 9. Lay down a 2" x 2" square over spaces 23, 24, 29 and 30

Step 10. Lay down a 2" x 2" square over spaces 28, 29, 34 and 35

Step 11. Lay down a 1.41" x 1.41" squares (i.e. square root of 2 x
square root of 2, with 2" diagonals) in a diamond configuration
directly over spaces 11, 12, 17, 18

Step 12. Lay down a 1.41" x 1.41" squares (i.e. square root of 2 x
square root of 2, with 2" diagonals) in a diamond configuration
directly over spaces 15, 16, 21, 22

Step 13. Lay down a 1.41" x 1.41" squares (i.e. square root of 2 x
square root of 2, with 2" diagonals) in a diamond configuration
directly over spaces 19, 20, 25, and 26

Step 14. Lay down 1" x 1" squares over spaces 13 and 27

[b***@yahoo.com]

Question 31. This question is a mainstay of mathematical puzzle books.
It can be solved by using a standard formula: An = An-1 + 2(n-1), where
A is the maximum number of pieces into which the sphere (or in this
case the onion) can be divided and n is the number of cuts. To generate
the number of pieces for six cuts, all you do is start with a single
cut and work your way up to six.

A single cut divides the onion into 2 pieces.
For 2 cuts: A = 2 + 2(2-1) = 4
For 3 cuts: A = 4 + 2(4-1) = 8
For 4 cuts: A = 8 + 2(4-1) =14
For 5 cuts: A = 14 + 2(5-1) = 22
For 6 cuts: A = 22 + 2(6-1) = 32

A full explanation is available at the following url:

http://www.math.washington.edu/~king/coursedir/m497w02/notes/notes3v2.html

[b***@yahoo.com]

Titan Question 34. Three interpenetrating circles yield a maximum of
seven pieces, not counting pieces that are further subdivided, as shown
to the right. What is the maximum number of pieces, not further
subdivided, that can be formed when three circles and two triangles all
interpenetrate?

How do you tackle a question like this? To recapitulate what my
calculus professor was wont to say some 25 years ago, "divide and
conquer." In other words, first look at the two types of geometric
figures (i.e., circles and triangles) as separate groups. See how many
pieces you can generate. Get a feel for the way they interpenetrate
with each other. Then try looking at all five figures simultaneously.

The question stem gets you started by informing you that three
interpenetring circles yield a maximum of 7 pieces. However, it is a
lot easier to start with the two triangles first and then superimpose
the circles on them. In a Star of David configuration, two
interpenetrating triangles can also yield 7 pieces. Using this as a
foundation, superimpose one circle on top of the six-pointed star so
that it passes through the middle of all six points. Then lay down a
second circle of the exact same size so that it is on top of the first
circle, but slightly north of it. The two circles should intersect at 3
o'clock and 9 o'clock in the area between points of the start. Now,
lay down a third circle on top of the first two circles so that it is
slightly east of the first circle. The first circle and third circle
should intersect at 6 o'clock and 12 o'clock. The second circle and
third circle should intersect at 1:30 and 7:30. If you count the
pieces, there should be 49.

[b***@yahoo.com]

Post by Puppet_Sock
[snip]

I had hoped that some of these proposed Titan puzzle answers would
generate discussion. But, it looks like the rec.puzzle subscribers are
not particularly cerebral. Maybe I'll post some urls for puzzle games
like "follow the dots."

[humunculus]

Really? That's what you hoped? Hmmm, what do you think went wrong?

I mean, other than the assumption that everyone here is beneath you and
your clever wit.

--riverman

[m***@aol.com]

Post by humunculus
Really? That's what you hoped? Hmmm, what do you think went wrong?
I mean, other than the assumption that everyone here is beneath you and
your clever wit.
--riverman

Just because a person can't get into the high IQ clubs doesn't
mean they aren't an elitist asshole.

[b***@yahoo.com]

Okay, so maybe you're an elitist. Perhaps, you should go back and read
through the entire thread before spreading your cheeks.

Post by m***@aol.com

Post by humunculus
Really? That's what you hoped? Hmmm, what do you think went wrong?
I mean, other than the assumption that everyone here is beneath you and
your clever wit.
--riverman

Just because a person can't get into the high IQ clubs doesn't
mean they aren't an elitist asshole.

[m***@aol.com]

Post by b***@yahoo.com
Okay, so maybe you're an elitist.

That was directed at you. No wonder they won't let you in their club,
no morons need apply.

As for the rest of the thread, what, exactly, do you think you are
accomplishing by posting the answers to the Titan Test? Do you
think the quack who charges $50 to score the test cares? He's
laughing all the way to the bank.

Do you think this will somehow discredit the Mega Society?
The Mega Society is a fraud and they admit such in their own
journal. They're not fooling anyone.

Anyone who isn't a top-posting dumbass.

[b***@yahoo.com]

Post by m***@aol.com

Post by b***@yahoo.com
Okay, so maybe you're an elitist.

That was directed at you.

Yes, obviously you meant to direct the comment at me. But, it's
projection on your part.

I mean, what kind of a loser would use a handle like "mensanator"? A
wanna be who could never get into Mensa or any other club of the same
genre?

After reviewing a few of your countless past postings, I don't think
I've ever encountered anyone who has posted as much useless crap.

[m***@aol.com]

Post by b***@yahoo.com

Post by m***@aol.com

Post by b***@yahoo.com
Okay, so maybe you're an elitist.

That was directed at you.

Yes, obviously you meant to direct the comment at me. But, it's
projection on your part.

Let's see, you barge into this newsgroup with your off-topic posts,
your cyber-vandalism and your insults. And when someone calls
you on this you accuse them of projection. Do you think there is
anyone stupid enough to believe that?

Post by b***@yahoo.com
I mean, what kind of a loser would use a handle like "mensanator"?

The word is meant as mockery, such as calling Arnold Schwartzenegger
"The Governator". It means "the one who put the Mensa in their
place by whipping their asses in their own Quiz Bowl competition".
But that doesn't roll off the tongue easily, so I usually opt for the
more whimsical "Slayer of the Mensa".

Post by b***@yahoo.com
A
wanna be who could never get into Mensa or any other club of the same
genre?

I neither need nor want the stigma of membership in some club
founded on quack psychology. And you have not yet answered
my question on what YOUR motivations are.

Post by b***@yahoo.com
After reviewing a few of your countless past postings, I don't think
I've ever encountered anyone who has posted as much useless crap.

Sturgeon's Law: 90% of everything is crap.

You've obviously not tried hard enough.

[swp]

please stop feeding the troll

[m***@aol.com]

Post by swp
please stop feeding the troll

12 consecutive posts without a single reply.

Feeding doesn't appear to be an issue, does it?

[b***@yahoo.com]

Post by m***@aol.com
Let's see, you barge into this newsgroup with your off-topic posts,

If you went back and re-read the entire thread, as I suggested you do
earlier, you would realize that I was building on a thread that was
already well developed by what were evidently some of the more regular
newsgroup participants. Hence, the post is hardly off-topic ... or out
of the blue (pardon the double entendre). That said, given the apparent
lack of interest, I won't bother posting any more explanations ...
although they were in keeping with the objectives of the person who
started the original thread.

Post by m***@aol.com

Post by b***@yahoo.com
I mean, what kind of a loser would use a handle like "mensanator"?

The word is meant as mockery, such as calling Arnold Schwartzenegger
"The Governator". It means "the one who put the Mensa in their
place by whipping their asses in their own Quiz Bowl competition".
But that doesn't roll off the tongue easily, so I usually opt for the
more whimsical "Slayer of the Mensa".

I hate to break it to you, but your rationale for the nickname of
"Mensanator" is illogical. This should be apparent if you consider
the following analogy:

Exterminator: One who exterminates :: Mensanator : ???

Plausible answers might be "one who mensanates" or "one who
strives to emulate Mensans."

You were probably thinking "one who exterminates Mensans", but that
interpretation is incorrect. I mean, what is a governator? Someone who
exterminates governors??

That said, if you like puzzles, and are halfway decent at them, why not
see if you can solve Titan question 27 in under 15 tiles? (probably
best if you didn't spend too much time with the analogies though).

[b***@yahoo.com]

Post by b***@yahoo.com

Post by m***@aol.com

Post by b***@yahoo.com
I mean, what kind of a loser would use a handle like "mensanator"?

The word is meant as mockery, such as calling Arnold Schwartzenegger
"The Governator". It means "the one who put the Mensa in their
place by whipping their asses in their own Quiz Bowl competition".
But that doesn't roll off the tongue easily, so I usually opt for the
more whimsical "Slayer of the Mensa".

I hate to break it to you, but your rationale for the nickname of
"Mensanator" is illogical. This should be apparent if you consider
Exterminator: One who exterminates :: Mensanator : ???
You were probably thinking "one who exterminates Mensans", but that
interpretation is incorrect. I mean, what is a governator? Someone who
exterminates governors??
That said, if you like puzzles, and are halfway decent at them, why not
see if you can solve Titan question 27 in under 15 tiles? (probably
best if you didn't spend too much time with the analogies though).

Hmm, I guess even the puzzle questions were too much for Mensanator?
... who professes the laughable (uhh ... I meant to say laudable, but
that just wouldn't come out) accomplishment of having "[whipped the
asses of Mensans] in their own Quiz Bowl competition." Anyway, I did
want to finish this thread by explaining how to solve the set of five
Titan test questions concerning ants and vertices.

[m***@aol.com]

Post by b***@yahoo.com

Post by b***@yahoo.com

Post by m***@aol.com

Post by b***@yahoo.com
I mean, what kind of a loser would use a handle like "mensanator"?

The word is meant as mockery, such as calling Arnold Schwartzenegger
"The Governator". It means "the one who put the Mensa in their
place by whipping their asses in their own Quiz Bowl competition".
But that doesn't roll off the tongue easily, so I usually opt for the
more whimsical "Slayer of the Mensa".

I hate to break it to you, but your rationale for the nickname of
"Mensanator" is illogical. This should be apparent if you consider
Exterminator: One who exterminates :: Mensanator : ???
You were probably thinking "one who exterminates Mensans", but that
interpretation is incorrect. I mean, what is a governator? Someone who
exterminates governors??

It's not a real word. I made it up. I can assign any meaning to it
I choose. Duh.

Post by b***@yahoo.com

Post by b***@yahoo.com
That said, if you like puzzles, and are halfway decent at them, why not
see if you can solve Titan question 27 in under 15 tiles?

Why? So I can be a cyber-vandal like you?

Post by b***@yahoo.com

Post by b***@yahoo.com
(probably
best if you didn't spend too much time with the analogies though).

Hmm, I guess even the puzzle questions were too much for Mensanator?

Not if I don't try. You're not very bright, are you?

Post by b***@yahoo.com
... who professes the laughable (uhh ... I meant to say laudable, but
that just wouldn't come out) accomplishment of having "[whipped the
asses of Mensans] in their own Quiz Bowl competition."

Why is it laughable? The Quiz Bowl is a trivia contest, not an
intelligence test. What's laughable is that Mensa play it. Don't you
see the irony in my having beaten the Mensa in a trivia contest?
Or is irony too big a concept for you to grasp?

Post by b***@yahoo.com
Anyway, I did
want to finish this thread by explaining how to solve the set of five
Titan test questions concerning ants and vertices.

Like anyone cares.

[Gareth Owen]

Post by m***@aol.com
Why is it laughable? The Quiz Bowl is a trivia contest, not an
intelligence test. What's laughable is that Mensa play it. Don't you
see the irony in my having beaten the Mensa in a trivia contest?

I don't see any irony.
Would it be ironic to beat the world darts champion at snooker?

Please explain to me why beating Mensa members at trivia contains irony.

[m***@aol.com]

Post by Gareth Owen

Post by m***@aol.com
Why is it laughable? The Quiz Bowl is a trivia contest, not an
intelligence test. What's laughable is that Mensa play it. Don't you
see the irony in my having beaten the Mensa in a trivia contest?

I don't see any irony.
Would it be ironic to beat the world darts champion at snooker?

It would if the darts champion thinks that being good at darts
means he should be good at snooker.

Post by Gareth Owen
Please explain to me why beating Mensa members at trivia contains irony.

Because of how seriously they took the loss, like it meant something.

And when I say "beaten them at their own game" I mean I was
able to prevail DESPITE the fact that the proctor had rigged the
deck of questions in favor of his friends. It just so happened that
at the critical moment in the contest when the rigged question was
thrown to me, I knew the answer. The proctors machinations
backfired and the interlopers won the tournament.

And guess what, the next year the proctor threw out his deck
of index cards that he'd been using for years, replaced all the
questions and changed the contest rules. All because I had won.

Which I enjoyed immensely, taught that bastard a lesson. We didn't
win under the new system, but we didn't care. We are the ultimate
champions under the original system.

[Gareth Owen]

Post by m***@aol.com

Post by Gareth Owen
Please explain to me why beating Mensa members at trivia contains irony.

Because of how seriously they took the loss, like it meant something.

I still don't see how this would constitute irony.
Are you using the word in its Morrissette declension?

[m***@aol.com]

Post by Gareth Owen

Post by m***@aol.com

Post by Gareth Owen
Please explain to me why beating Mensa members at trivia contains irony.

Because of how seriously they took the loss, like it meant something.

I still don't see how this would constitute irony.

<quote>
The American Heritage® Dictionary of the English Language: Fourth
Edition. 2000.

ironic

ADJECTIVE: 1. Characterized by or constituting irony.
2. Given to the use of irony. See synonyms at sarcastic.
3. Poignantly contrary to what was expected or intended:
madness, an ironic fate for such a clear thinker.

USAGE NOTE: <non-ironic example snipped>

By contrast, 73 percent accepted the sentence
Ironically, even as the government was
fulminating against American policy,
American jeans and videocassettes were
the hottest items in the stalls of the
market
where the incongruity can be seen as an example
of human inconsistency.
</quote>

Post by Gareth Owen
Are you using the word in its Morrissette declension?

I say that the proctor's attempt to protect his turf is ironic because
a trivia test is not an intelligence test.

[Puppet_Sock]

***@yahoo.com wrote:
[snip]

Post by j***@yahoo.com
6. ALL IS ONE : MONISM :: ALL IS SELF : SOLIPSISM (a doctrine in
philosophy, nothing exists except the self, or alternately the
existence of everything else depends on the existence of the self)

I've long wondered why there are not more solipsists.
Socks

[Willem]

Puppet_Sock wrote:
) ***@yahoo.com wrote:
) [snip]
)> 6. ALL IS ONE : MONISM :: ALL IS SELF : SOLIPSISM (a doctrine in
)> philosophy, nothing exists except the self, or alternately the
)> existence of everything else depends on the existence of the self)
)
) I've long wondered why there are not more solipsists.
) Socks

Nonsense. By the very nature of Solipsism, there's only one solipsist.


SaSW, Willem

[Wilbur Slice]

Post by Willem
) [snip]
)> 6. ALL IS ONE : MONISM :: ALL IS SELF : SOLIPSISM (a doctrine in
)> philosophy, nothing exists except the self, or alternately the
)> existence of everything else depends on the existence of the self)
)
) I've long wondered why there are not more solipsists.
) Socks
Nonsense. By the very nature of Solipsism, there's only one solipsist.

Sure, but there's a LOT of those "only ones".

[Puppet_Sock]

Post by Willem
) [snip]
)> 6. ALL IS ONE : MONISM :: ALL IS SELF : SOLIPSISM (a doctrine in
)> philosophy, nothing exists except the self, or alternately the
)> existence of everything else depends on the existence of the self)
)
) I've long wondered why there are not more solipsists.
) Socks
Nonsense. By the very nature of Solipsism, there's only one solipsist.

Do nihilsts believe in nihilsm?
Socks

[Matthew Russotto]

Post by Willem
) [snip]
)> 6. ALL IS ONE : MONISM :: ALL IS SELF : SOLIPSISM (a doctrine in
)> philosophy, nothing exists except the self, or alternately the
)> existence of everything else depends on the existence of the self)
)
) I've long wondered why there are not more solipsists.
Nonsense. By the very nature of Solipsism, there's only one solipsist.

I'm a solipsist-by-proxy. Same as solipsism, except it's someone
else's self which exists.

[h***@gmail.com]

Question
50. So what the hell makes my IQ quark 1>250

Answer
PI

Note* using all factors of my age race Education my extermly artistic nature as well as dumbing down questions of known and unknown subjects. The titan test took me less than 2 minutes and clearly if u understand PI then you can claim my score. I loved the fact that i cleared the known 230 of da vinci by 20 pionts that means 600 years later 33.3333333% increase in universal intelligence at the rate of appox...6 points per every 200 years. Wow we as a whole are still pretty dumb. Although I will produce art works 33% better than that of even carriviggo. Sorry buddy. If your trying to reach the boundary level of my quark 1>250 dont get stuck on sceince to long because even they miss there simplified 10π32. Which really is the answer to there #1 ? How do u miss your own answer?? Lol cause they forget reason instead they ponder. Hehehe

[j***@gmail.com]

Post by j***@yahoo.com
If you spot an error or would like to add answers, please reply to this
post or send me an e-mail, or both.

Question 25 can be completed with 6 squares instead of 9.

Imagine a 4 by 4 Grid such as the following:

* A B C D
1
2
3
4


For the 1st and bottom-most layer we have 1A to 4D
For the 2nd layer we have 1A to 3C
For the 3rd we have 2A to 2D
For the 4th we have 1B to 4B
For the 5th, 2C to 3C
And for the final layer, we have a square rotated 45 degrees as a diamond from 2B to 3C


2 4 2 1
3 4 5 3
2 4 5 1
1 4 1 1

Then with the 6th layer being the diamond.

2 4 2 1
3 6 6 3
2 6 6 1
1 4 1 1

[a***@gmail.com]

Hey gents,

If anyone is still reading this thread, I would like to add some input. I recently found the Titan Test online and found it to be a great mental challenge. Now, I agree with most of the answers provided for both the verbal analogies and the spatial/quantitative problems. However, I have some feedback that may(?) be helpful if anyone is still interested.

19. Cosmonomologo- ? I have never heard this before. I haven't even seen it, despite some astrophysics at the undergraduate level. If this is a true prefix, I'm impressed you guys found it.

20. I know initially you said some suggested Kessler as an answer, but seeing as how the "set of sets not members of themselves" or the naive set is called Russell's paradox, I think Olbers indeed fits better here as the "darkness of the night sky" phenomenon is typically referred to as the "Olbers Parabox" and not the Kessler paradox.

24. Similarly, I believe the -swain on 'boatswain' is more a suprafix than stem. Suprafix a linguistic term referring to an affix that, in so many words, effects a tonal or stress change on a given word. While 'stem' and 'base' both fit a sort of sing-song linguistic pattern sought in many of the "correct" (possibly) answers to other analogies, I believe that 'suprafix' fits both a definition-based and linguistic pattern better than the other two propositions.

25. I have to agree with the initial 9-square construction. Though I like the minimalist solutions posited by j.poll above, the shapes you used to construct the solution were not all squares. I have to concede to 9. I got the same answer when doing this one independently, and though the most common answer is not always the most correct, I took the instructions literally and only used squares for my answers.

33. I found this to be the most interesting, and, subsequently, most difficult problem on the test. I had to do some really mind-stretching geometric thinking to wrap my brain around the concept of first excising the Mobius Strip, then the concept of the two pieces (the Mobius Strip and the two-sided orientable surface left behind), then the concept of the pieces being unmoved, so that subsequent cuts sliced both pieces, despite only one yielding subsequent Mobius Strips.

Firstly, the first cut can only yield two pieces, and, interestingly enough, one is a one-sided surface, the Mobius Strip, and the other is an orientable loop. However, the second cut gets more interesting.

In order to excise another Mobius Strip, you either have to cut the same pattern into the torus, shifted laterally to provide enough room for the cut, or you have to cut the interior of the first Mobius strip in two 360 degree, circumferential motions to excise a similar Mobius from the first. I opted for the second method of slicing for two reasons: (1) it maximizes the number of pieces from excision (and we are looking for a maximum here) and (2) while the first method cuts a second Mobius pattern in the same way as the first cut, it doesn't actually yield a Mobius Strip because the excision of the first strip gets in the way, so to speak, interfering with a whole remaining Mobius Strip.

I then decided to 'unroll' the Torus, looking at it as a topologist would, as a solid cylinder, rather than a donut-shaped solid surface. For me, it was just easier that way. When you do this, you would see that the first method of cutting would be possible, yielding another Mobius strip, but ultimately, after three cuts, one would only have four whole pieces, which, intuitively, seems low for this exercise.

Keeping the torus 'unrolled,' you can see that the second method of slicing the torus (on the second and third slices, at least) would render the knife perpendicular to the singular side of the Mobius on both circumferential motions. I say motions here, because even though to cut in this manner, you are traversing the arc of the torus twice, you are doing it in one smooth cut, never tracing over the path of your previous traverse in the second or third cuts. This method cuts the interior Mobius Strip of the first cut into two remaining surfaces, again another Mobius Strip, and an orientable loop, much like the remnant surface of the first cut.

However, because the pieces are never moved from their original positions, the double-circumferential second cut slices this surface along the way. As an aside, this is all much easier to visualize as a solid cylinder with the appropriate equivalences on the edges of the cylinder, rather than as an intact torus. As a result of the second cut using my second method, there are now 8 subdivided pieces instead of 4, so it is, indeed, a maximum producing cut. The pieces are, using the first cut as an 'axis' for orientation, the six subdivided pieces of the coiled orientable complement of the Mobius rendered in the first cut, (three 'above and 'below' the Mobius---again, this is easier to view in an un-coiled cylinder), the new Mobius Strip cut from the interior of the extant Mobius Strip, and the complement orientable surface (8 total after two cuts).

Now, the third cut will follow the pattern of the second, in terms of excision via a double-traversed circumferential arc. It will however, excise the middle of the Mobius Strip rendered by the second cut. This will render two additional pieces from the central Mobius of the second cut, and will render two of the three axial cuts from the first orientable two-sided surface, into three pieces. This leave, the new (third) Mobius, the new (third) orientable complement, and the original Mobius strip, which has been quadruply-traversed to yield two new Mobius Strips. The 'axial' orientations withstanding, 'above' and 'below' the original Mobius, there are five remaining on each axial orientation: one initial 'slice' leaving one piece after the first cut, the second cut leaving six, after the double-traverse rendered this single slice into 'thirds', and another double-traverse slicing the middle 'third' into three more pieces. So on each axial orientation, there are five remaining pieces, i.e. ten altogether. These ten, coupled with the three progressively sliced Mobii (?) leaves 13.

Now, the real challenge is assessing the equivalence of my method of slicing with the question: to rehash the question's key challenge "a knife that each time precisely follows the path of such a Möbius strip. What is the maximum number of pieces that can result if the pieces are never moved from their original positions"

The nuts and bolts are: is the knife required to make the same cutting pattern each time, in which case an oriented shift to 'offset' subsequent Mobius Strips would simply maximize the pieces yielded from their intersections. If we 'unroll' the torus, keeping in mind the equivalence relation on the edges of our new cylinder, then we can see that what I present as the second cutting method above, is actually equivalent to the knife pattern of the first cut, it just has a perpendicular orientation to the first cut, ie a normal orientation to the surface of the initial Mobius strip! If we focus on the Mobius and its effect on the torus as a whole, we lose the real meat and potatoes of the subsequent slices. We have to start, visually, from after the first cut, which is where things got really interesting.

I understand this is a discussion forum and that I may be entirely off-base or wrong altogether. I did, however, get the number 13, which is interesting in and of itself. So, in the habit of good-spirited academic collaboration, discuss away!

[a***@gmail.com]

And by Kessler, I of course meant Kepler...woops!

Post by a***@gmail.com
Hey gents,
If anyone is still reading this thread, I would like to add some input. I recently found the Titan Test online and found it to be a great mental challenge. Now, I agree with most of the answers provided for both the verbal analogies and the spatial/quantitative problems. However, I have some feedback that may(?) be helpful if anyone is still interested.
19. Cosmonomologo- ? I have never heard this before. I haven't even seen it, despite some astrophysics at the undergraduate level. If this is a true prefix, I'm impressed you guys found it.
20. I know initially you said some suggested Kessler as an answer, but seeing as how the "set of sets not members of themselves" or the naive set is called Russell's paradox, I think Olbers indeed fits better here as the "darkness of the night sky" phenomenon is typically referred to as the "Olbers Parabox" and not the Kessler paradox.
24. Similarly, I believe the -swain on 'boatswain' is more a suprafix than stem. Suprafix a linguistic term referring to an affix that, in so many words, effects a tonal or stress change on a given word. While 'stem' and 'base' both fit a sort of sing-song linguistic pattern sought in many of the "correct" (possibly) answers to other analogies, I believe that 'suprafix' fits both a definition-based and linguistic pattern better than the other two propositions.
25. I have to agree with the initial 9-square construction. Though I like the minimalist solutions posited by j.poll above, the shapes you used to construct the solution were not all squares. I have to concede to 9. I got the same answer when doing this one independently, and though the most common answer is not always the most correct, I took the instructions literally and only used squares for my answers.
33. I found this to be the most interesting, and, subsequently, most difficult problem on the test. I had to do some really mind-stretching geometric thinking to wrap my brain around the concept of first excising the Mobius Strip, then the concept of the two pieces (the Mobius Strip and the two-sided orientable surface left behind), then the concept of the pieces being unmoved, so that subsequent cuts sliced both pieces, despite only one yielding subsequent Mobius Strips.
Firstly, the first cut can only yield two pieces, and, interestingly enough, one is a one-sided surface, the Mobius Strip, and the other is an orientable loop. However, the second cut gets more interesting.
In order to excise another Mobius Strip, you either have to cut the same pattern into the torus, shifted laterally to provide enough room for the cut, or you have to cut the interior of the first Mobius strip in two 360 degree, circumferential motions to excise a similar Mobius from the first. I opted for the second method of slicing for two reasons: (1) it maximizes the number of pieces from excision (and we are looking for a maximum here) and (2) while the first method cuts a second Mobius pattern in the same way as the first cut, it doesn't actually yield a Mobius Strip because the excision of the first strip gets in the way, so to speak, interfering with a whole remaining Mobius Strip.
I then decided to 'unroll' the Torus, looking at it as a topologist would, as a solid cylinder, rather than a donut-shaped solid surface. For me, it was just easier that way. When you do this, you would see that the first method of cutting would be possible, yielding another Mobius strip, but ultimately, after three cuts, one would only have four whole pieces, which, intuitively, seems low for this exercise.
Keeping the torus 'unrolled,' you can see that the second method of slicing the torus (on the second and third slices, at least) would render the knife perpendicular to the singular side of the Mobius on both circumferential motions. I say motions here, because even though to cut in this manner, you are traversing the arc of the torus twice, you are doing it in one smooth cut, never tracing over the path of your previous traverse in the second or third cuts. This method cuts the interior Mobius Strip of the first cut into two remaining surfaces, again another Mobius Strip, and an orientable loop, much like the remnant surface of the first cut.
However, because the pieces are never moved from their original positions, the double-circumferential second cut slices this surface along the way. As an aside, this is all much easier to visualize as a solid cylinder with the appropriate equivalences on the edges of the cylinder, rather than as an intact torus. As a result of the second cut using my second method, there are now 8 subdivided pieces instead of 4, so it is, indeed, a maximum producing cut. The pieces are, using the first cut as an 'axis' for orientation, the six subdivided pieces of the coiled orientable complement of the Mobius rendered in the first cut, (three 'above and 'below' the Mobius---again, this is easier to view in an un-coiled cylinder), the new Mobius Strip cut from the interior of the extant Mobius Strip, and the complement orientable surface (8 total after two cuts).
Now, the third cut will follow the pattern of the second, in terms of excision via a double-traversed circumferential arc. It will however, excise the middle of the Mobius Strip rendered by the second cut. This will render two additional pieces from the central Mobius of the second cut, and will render two of the three axial cuts from the first orientable two-sided surface, into three pieces. This leave, the new (third) Mobius, the new (third) orientable complement, and the original Mobius strip, which has been quadruply-traversed to yield two new Mobius Strips. The 'axial' orientations withstanding, 'above' and 'below' the original Mobius, there are five remaining on each axial orientation: one initial 'slice' leaving one piece after the first cut, the second cut leaving six, after the double-traverse rendered this single slice into 'thirds', and another double-traverse slicing the middle 'third' into three more pieces. So on each axial orientation, there are five remaining pieces, i.e. ten altogether. These ten, coupled with the three progressively sliced Mobii (?) leaves 13.
Now, the real challenge is assessing the equivalence of my method of slicing with the question: to rehash the question's key challenge "a knife that each time precisely follows the path of such a Möbius strip. What is the maximum number of pieces that can result if the pieces are never moved from their original positions"
The nuts and bolts are: is the knife required to make the same cutting pattern each time, in which case an oriented shift to 'offset' subsequent Mobius Strips would simply maximize the pieces yielded from their intersections. If we 'unroll' the torus, keeping in mind the equivalence relation on the edges of our new cylinder, then we can see that what I present as the second cutting method above, is actually equivalent to the knife pattern of the first cut, it just has a perpendicular orientation to the first cut, ie a normal orientation to the surface of the initial Mobius strip! If we focus on the Mobius and its effect on the torus as a whole, we lose the real meat and potatoes of the subsequent slices. We have to start, visually, from after the first cut, which is where things got really interesting.
I understand this is a discussion forum and that I may be entirely off-base or wrong altogether. I did, however, get the number 13, which is interesting in and of itself. So, in the habit of good-spirited academic collaboration, discuss away!

[c***@gmail.com]

The solution to 19 is certainly NOMO- as in "nomological" (http://en.wiktionary.org/wiki/nomological).

I also agree that SUPRAFIX is correct.

In an old issue of Noesis, the journal of the Mega Society, they discuss the mobius strips in a torus problem. Here is a link to that issue: http://megasociety.org/noesis/60.htm

The editor writes, "I know Ron Hoeflin doesn't like answers to his tests floating around, so in this and the following letters, I've mixed the answer to prob 33 with a few dummy answers. I hope this is a reasonable compromise."

In the paragraph where they discuss the version of the problem in which the mobius strips are confined to the interior of the torus, i.e., the version of the problem used in the latest version of the Titan Test, the possible solutions given are: 4, 8, 17, 36.

You got 13, so if you counted correctly, the accepted answer cannot be 4 or 8. 17 seems most likely to be correct, unless you overlooked something big. In any case, I haven't checked your work or tried the problem myself.

[r***@yahoo.com]

Post by a***@gmail.com
Hey gents,
If anyone is still reading this thread, I would like to add some input. I recently found the Titan Test online and found it to be a great mental challenge. Now, I agree with most of the answers provided for both the verbal analogies and the spatial/quantitative problems. However, I have some feedback that may(?) be helpful if anyone is still interested.
19. Cosmonomologo- ? I have never heard this before. I haven't even seen it, despite some astrophysics at the undergraduate level. If this is a true prefix, I'm impressed you guys found it.
20. I know initially you said some suggested Kessler as an answer, but seeing as how the "set of sets not members of themselves" or the naive set is called Russell's paradox, I think Olbers indeed fits better here as the "darkness of the night sky" phenomenon is typically referred to as the "Olbers Parabox" and not the Kessler paradox.
24. Similarly, I believe the -swain on 'boatswain' is more a suprafix than stem. Suprafix a linguistic term referring to an affix that, in so many words, effects a tonal or stress change on a given word. While 'stem' and 'base' both fit a sort of sing-song linguistic pattern sought in many of the "correct" (possibly) answers to other analogies, I believe that 'suprafix' fits both a definition-based and linguistic pattern better than the other two propositions.
25. I have to agree with the initial 9-square construction. Though I like the minimalist solutions posited by j.poll above, the shapes you used to construct the solution were not all squares. I have to concede to 9. I got the same answer when doing this one independently, and though the most common answer is not always the most correct, I took the instructions literally and only used squares for my answers.
33. I found this to be the most interesting, and, subsequently, most difficult problem on the test. I had to do some really mind-stretching geometric thinking to wrap my brain around the concept of first excising the Mobius Strip, then the concept of the two pieces (the Mobius Strip and the two-sided orientable surface left behind), then the concept of the pieces being unmoved, so that subsequent cuts sliced both pieces, despite only one yielding subsequent Mobius Strips.
Firstly, the first cut can only yield two pieces, and, interestingly enough, one is a one-sided surface, the Mobius Strip, and the other is an orientable loop. However, the second cut gets more interesting.
In order to excise another Mobius Strip, you either have to cut the same pattern into the torus, shifted laterally to provide enough room for the cut, or you have to cut the interior of the first Mobius strip in two 360 degree, circumferential motions to excise a similar Mobius from the first. I opted for the second method of slicing for two reasons: (1) it maximizes the number of pieces from excision (and we are looking for a maximum here) and (2) while the first method cuts a second Mobius pattern in the same way as the first cut, it doesn't actually yield a Mobius Strip because the excision of the first strip gets in the way, so to speak, interfering with a whole remaining Mobius Strip.
I then decided to 'unroll' the Torus, looking at it as a topologist would, as a solid cylinder, rather than a donut-shaped solid surface. For me, it was just easier that way. When you do this, you would see that the first method of cutting would be possible, yielding another Mobius strip, but ultimately, after three cuts, one would only have four whole pieces, which, intuitively, seems low for this exercise.
Keeping the torus 'unrolled,' you can see that the second method of slicing the torus (on the second and third slices, at least) would render the knife perpendicular to the singular side of the Mobius on both circumferential motions. I say motions here, because even though to cut in this manner, you are traversing the arc of the torus twice, you are doing it in one smooth cut, never tracing over the path of your previous traverse in the second or third cuts. This method cuts the interior Mobius Strip of the first cut into two remaining surfaces, again another Mobius Strip, and an orientable loop, much like the remnant surface of the first cut.
However, because the pieces are never moved from their original positions, the double-circumferential second cut slices this surface along the way. As an aside, this is all much easier to visualize as a solid cylinder with the appropriate equivalences on the edges of the cylinder, rather than as an intact torus. As a result of the second cut using my second method, there are now 8 subdivided pieces instead of 4, so it is, indeed, a maximum producing cut. The pieces are, using the first cut as an 'axis' for orientation, the six subdivided pieces of the coiled orientable complement of the Mobius rendered in the first cut, (three 'above and 'below' the Mobius---again, this is easier to view in an un-coiled cylinder), the new Mobius Strip cut from the interior of the extant Mobius Strip, and the complement orientable surface (8 total after two cuts).
Now, the third cut will follow the pattern of the second, in terms of excision via a double-traversed circumferential arc. It will however, excise the middle of the Mobius Strip rendered by the second cut. This will render two additional pieces from the central Mobius of the second cut, and will render two of the three axial cuts from the first orientable two-sided surface, into three pieces. This leave, the new (third) Mobius, the new (third) orientable complement, and the original Mobius strip, which has been quadruply-traversed to yield two new Mobius Strips. The 'axial' orientations withstanding, 'above' and 'below' the original Mobius, there are five remaining on each axial orientation: one initial 'slice' leaving one piece after the first cut, the second cut leaving six, after the double-traverse rendered this single slice into 'thirds', and another double-traverse slicing the middle 'third' into three more pieces. So on each axial orientation, there are five remaining pieces, i.e. ten altogether. These ten, coupled with the three progressively sliced Mobii (?) leaves 13.
Now, the real challenge is assessing the equivalence of my method of slicing with the question: to rehash the question's key challenge "a knife that each time precisely follows the path of such a Möbius strip. What is the maximum number of pieces that can result if the pieces are never moved from their original positions"
The nuts and bolts are: is the knife required to make the same cutting pattern each time, in which case an oriented shift to 'offset' subsequent Mobius Strips would simply maximize the pieces yielded from their intersections. If we 'unroll' the torus, keeping in mind the equivalence relation on the edges of our new cylinder, then we can see that what I present as the second cutting method above, is actually equivalent to the knife pattern of the first cut, it just has a perpendicular orientation to the first cut, ie a normal orientation to the surface of the initial Mobius strip! If we focus on the Mobius and its effect on the torus as a whole, we lose the real meat and potatoes of the subsequent slices. We have to start, visually, from after the first cut, which is where things got really interesting.
I understand this is a discussion forum and that I may be entirely off-base or wrong altogether. I did, however, get the number 13, which is interesting in and of itself. So, in the habit of good-spirited academic collaboration, discuss away!

[b***@gmail.com]

I think the answer to 16 is "orbital" - these are bones.

[c***@gmail.com]

Where do I see the answers to the Titan Test? https://www.quora.com/Is-the-Titan-Test-still-the-premiere-intellectual-quiz

Post by j***@yahoo.com
If you spot an error or would like to add answers, please reply to this
post or send me an e-mail, or both.
Don't forget to explain your answer, the more detail the better.
http://www.eskimo.com/~miyaguch/titan.html
1. STRIP : MoBIUS :: BOTTLE : KLEIN
2. THOUGHT : ACTION :: OBSESSIVE : COMPULSIVE
3. LACKING MONEY : PENURIOUS :: DOTING ON ONE'S WIFE : UXORIOUS
(definitions)
4. MICE : MEN :: CABBAGES : KINGS (from literature)
5. TIRE : RETREAD :: PARCHMENT : PALIMPSEST
6. ALL IS ONE : MONISM :: ALL IS SELF : SOLIPSISM (a doctrine in
philosophy, nothing exists except the self, or alternately the
existence of everything else depends on the existence of the self)
7. SWORD : DAMOCLES :: BED : PROCRUSTES
8. THING : DANGEROUS :: SPRING : PIERIAN
(A little learning is a dangerous thing; drink deep, or taste not the
Pierian spring - Alexander Pope. An
Essay on Criticism)
9. HOLLOW VICTORY : PYRRHIC :: HOLLOW VILLAGE : Potemkin
10. PILLAR : OBELISK :: MONSTER : BASILISK (OBELISK from Greek
obeliskos, BASILISK from Greek basiliskos)
11. 4 : HAND :: 9 : SPAN (a hand is 4 inches, a span is 9 inches)
12. GOLD : MALLEABLE :: CHALK : FRIABLE (rhyming pattern)
13. EASY JOB : SINECURE :: GUIDING LIGHT : CYNOSURE (the rhyming
pattern is the key here)
14. LEG : AMBULATE :: ARM : BRACHIATE
15. MOSQUITO : MALARIA :: CANNIBALISM : KURU (a disease limited to the
Fore tribe of New Guinea, who eat human brain in their religious
rituals)
16. HEAR : SEE :: TEMPORAL : OCCIPITAL (Lobes of the brain that deal
with hearing and sight.
CLIOMETRICS (Cliometrics is the use of statistics or economics in
historical studies.)
18. JEKYLL : HYDE :: ELOI : MORLOCKS (from the books by Robert Louis
Stevenson and H.G. Wells)
19. UNIVERSE : COSMO- :: UNIVERSAL LAWS : COSMONOMOLOGO-
20. SET OF SETS NOT MEMBERS OF THEMSELVES : RUSSELL :: DARKNESS OF THE
NIGHT SKY IN AN INFINITE UNIVERSE : OLBERS
(KEPLER has also been offered as an answer)
21. TEACHING : UPLIFTING :: PEDAGOGIC : ANAGOGIC (from Greek
for spiritual uplift)
22. LANGUAGE GAMES : LUDWIG :: PIANO CONCERTI FOR THE LEFT HAND : PAUL
(So obscure it is silly. Ludwig and Paul Wittgenstein were brothers.
One was a pianist, the other was the famous philosopher who used the
phrase "language games" in his book Philosophical Investigations.
Knowing this meaningless bit of trivia can hardly be an indication of
great intelligence.)
23. IDOLS : TWILIGHT :: MORALS : GENEALOGY (Titles of Nietzsche's
books)
24. SWEET*NESS* : SUFFIX :: BOAT*SWAIN* : STEM ("ness" is a suffix,
"swain" is the stem of the compound word "boatswain."
Alternate answer is BASE, which fits the rhyming pattern better
29. The answer is 20.
31. The answer is 22
(this answer may be wrong)
37.
Initially, we need to consider 11 possibilities where we choose 10
white marbles.
1) After the insertion, the box contains 10 whites. The chances of
this are 1 in 2^10, i.e. 1 in 1024. If this is the case, in our
subsequent drawing we're bound to pick out 10 whites. Total probability
of this possibility = 1/1024
2) After the insertion, the box contains 9 whites. The chances of this
are 10!/9!/1! = 10 in 1024. If this is the case, in our subsequent
drawing our chances of picking out 10 whites is (9/10)^10 because we
have a 9/10 chance each time. Total probability of this possibility =
10/1024 * (9/10)^10
3) After the insertion, the box contains 8 whites. The chances of this
are 10!/8!/2! = 45 in 1024. If this is the case, in our subsequent
drawing our chances of picking out 10 whites is (8/10)^10 because we
have a 8/10 chance each time. Total probability of this possibility =
45/1024 * (8/10)^10
4) Box = 7 whites. Total = 120/1024 * (7/10)^10 i.e. nCr * (r/10)^10
5) Box = 6 whites. Total = 210/1024 * (6/10)^10
6) Box = 5 whites. Total = 252/1024 * (5/10)^10
7) Box = 4 whites. Total = 210/1024 * (4/10)^10
8 ) Box = 3 whites. Total = 120/1024 * (3/10)^10
9) Box = 2 whites. Total = 45/1024 * (2/10)^10
10) Box = 1 whites. Total = 10/1024 * (1/10)^10
11) Box = 0 whites. Total = 1/1024 * (0/10)^10 = 0!!
So, the chances of drawing 10 whites is the sum of these which is
0.013913029625. Approximately. However, we know that we actually drew
10 whites, so this 1 in 72 (ish) chance has happened. The chance that
it happened because we had possibility 1) above is the chance of 1)
relative to this 0.0139... chance. So, the answer is
(1/1024)/0.013913029625 which is 0.070190499... i.e. 7%.
So there!
I suggest that the answer you have given is to the question "What is
the probability of you pulling out 10 white marbles one at a time?"
The question is, however, "what is the probability of all marbles being
white(or black)? The answer to that, I believe, is 1/1024, which to
nearest % is '0'.
I just re-read it, and I think I got it right. The question is, what is
the probability of them all being white, given that you randomly
withdrew and returned 10 white marbles consecutively.
38. 2 / 27
39. 8 / 3^7 or 4 / 3^27 (two solutions have been offered)
http://groups.google.com/group/rec.puzzles/msg/8b1875e5406828ff?dmode=source
45. -4697
x = n^3 - n!
2^3 = 8, 2! = 2 so 8-2 = 6
3^3 = 27, 3! = 6 so 27-6 = 21
4^3 = 64, 4! = 24 so 64-24 = 40...
46. 95,041,567
the numbers are all products of increasingly large numbers of
successive primes.
2 = 2 (or 2x1?),
15 = 3x5,
1001 = 7x11x13,
215,441 = 17x19x23x29
and I think the next in the series should be
95,041,567 = 31x37x41x43x47.
47. 3 (The list is of the digits of pi/4)
48. pi^2 r^4 / 2 The hyper-volume of a 4-dimensional hyper-sphere.

[c***@gmail.com]

Link to Titan Test https://www.scribd.com/document/387599049/Titan-Test#page=1&fullscreen=1

Post by j***@yahoo.com
If you spot an error or would like to add answers, please reply to this
post or send me an e-mail, or both.
Don't forget to explain your answer, the more detail the better.
http://www.eskimo.com/~miyaguch/titan.html
1. STRIP : MoBIUS :: BOTTLE : KLEIN
2. THOUGHT : ACTION :: OBSESSIVE : COMPULSIVE
3. LACKING MONEY : PENURIOUS :: DOTING ON ONE'S WIFE : UXORIOUS
(definitions)
4. MICE : MEN :: CABBAGES : KINGS (from literature)
5. TIRE : RETREAD :: PARCHMENT : PALIMPSEST
6. ALL IS ONE : MONISM :: ALL IS SELF : SOLIPSISM (a doctrine in
philosophy, nothing exists except the self, or alternately the
existence of everything else depends on the existence of the self)
7. SWORD : DAMOCLES :: BED : PROCRUSTES
8. THING : DANGEROUS :: SPRING : PIERIAN
(A little learning is a dangerous thing; drink deep, or taste not the
Pierian spring - Alexander Pope. An
Essay on Criticism)
9. HOLLOW VICTORY : PYRRHIC :: HOLLOW VILLAGE : Potemkin
10. PILLAR : OBELISK :: MONSTER : BASILISK (OBELISK from Greek
obeliskos, BASILISK from Greek basiliskos)
11. 4 : HAND :: 9 : SPAN (a hand is 4 inches, a span is 9 inches)
12. GOLD : MALLEABLE :: CHALK : FRIABLE (rhyming pattern)
13. EASY JOB : SINECURE :: GUIDING LIGHT : CYNOSURE (the rhyming
pattern is the key here)
14. LEG : AMBULATE :: ARM : BRACHIATE
15. MOSQUITO : MALARIA :: CANNIBALISM : KURU (a disease limited to the
Fore tribe of New Guinea, who eat human brain in their religious
rituals)
16. HEAR : SEE :: TEMPORAL : OCCIPITAL (Lobes of the brain that deal
with hearing and sight.
CLIOMETRICS (Cliometrics is the use of statistics or economics in
historical studies.)
18. JEKYLL : HYDE :: ELOI : MORLOCKS (from the books by Robert Louis
Stevenson and H.G. Wells)
19. UNIVERSE : COSMO- :: UNIVERSAL LAWS : COSMONOMOLOGO-
20. SET OF SETS NOT MEMBERS OF THEMSELVES : RUSSELL :: DARKNESS OF THE
NIGHT SKY IN AN INFINITE UNIVERSE : OLBERS
(KEPLER has also been offered as an answer)
21. TEACHING : UPLIFTING :: PEDAGOGIC : ANAGOGIC (from Greek
for spiritual uplift)
22. LANGUAGE GAMES : LUDWIG :: PIANO CONCERTI FOR THE LEFT HAND : PAUL
(So obscure it is silly. Ludwig and Paul Wittgenstein were brothers.
One was a pianist, the other was the famous philosopher who used the
phrase "language games" in his book Philosophical Investigations.
Knowing this meaningless bit of trivia can hardly be an indication of
great intelligence.)
23. IDOLS : TWILIGHT :: MORALS : GENEALOGY (Titles of Nietzsche's
books)
24. SWEET*NESS* : SUFFIX :: BOAT*SWAIN* : STEM ("ness" is a suffix,
"swain" is the stem of the compound word "boatswain."
Alternate answer is BASE, which fits the rhyming pattern better
29. The answer is 20.
31. The answer is 22
(this answer may be wrong)
37.
Initially, we need to consider 11 possibilities where we choose 10
white marbles.
1) After the insertion, the box contains 10 whites. The chances of
this are 1 in 2^10, i.e. 1 in 1024. If this is the case, in our
subsequent drawing we're bound to pick out 10 whites. Total probability
of this possibility = 1/1024
2) After the insertion, the box contains 9 whites. The chances of this
are 10!/9!/1! = 10 in 1024. If this is the case, in our subsequent
drawing our chances of picking out 10 whites is (9/10)^10 because we
have a 9/10 chance each time. Total probability of this possibility =
10/1024 * (9/10)^10
3) After the insertion, the box contains 8 whites. The chances of this
are 10!/8!/2! = 45 in 1024. If this is the case, in our subsequent
drawing our chances of picking out 10 whites is (8/10)^10 because we
have a 8/10 chance each time. Total probability of this possibility =
45/1024 * (8/10)^10
4) Box = 7 whites. Total = 120/1024 * (7/10)^10 i.e. nCr * (r/10)^10
5) Box = 6 whites. Total = 210/1024 * (6/10)^10
6) Box = 5 whites. Total = 252/1024 * (5/10)^10
7) Box = 4 whites. Total = 210/1024 * (4/10)^10
8 ) Box = 3 whites. Total = 120/1024 * (3/10)^10
9) Box = 2 whites. Total = 45/1024 * (2/10)^10
10) Box = 1 whites. Total = 10/1024 * (1/10)^10
11) Box = 0 whites. Total = 1/1024 * (0/10)^10 = 0!!
So, the chances of drawing 10 whites is the sum of these which is
0.013913029625. Approximately. However, we know that we actually drew
10 whites, so this 1 in 72 (ish) chance has happened. The chance that
it happened because we had possibility 1) above is the chance of 1)
relative to this 0.0139... chance. So, the answer is
(1/1024)/0.013913029625 which is 0.070190499... i.e. 7%.
So there!
I suggest that the answer you have given is to the question "What is
the probability of you pulling out 10 white marbles one at a time?"
The question is, however, "what is the probability of all marbles being
white(or black)? The answer to that, I believe, is 1/1024, which to
nearest % is '0'.
I just re-read it, and I think I got it right. The question is, what is
the probability of them all being white, given that you randomly
withdrew and returned 10 white marbles consecutively.
38. 2 / 27
39. 8 / 3^7 or 4 / 3^27 (two solutions have been offered)
http://groups.google.com/group/rec.puzzles/msg/8b1875e5406828ff?dmode=source
45. -4697
x = n^3 - n!
2^3 = 8, 2! = 2 so 8-2 = 6
3^3 = 27, 3! = 6 so 27-6 = 21
4^3 = 64, 4! = 24 so 64-24 = 40...
46. 95,041,567
the numbers are all products of increasingly large numbers of
successive primes.
2 = 2 (or 2x1?),
15 = 3x5,
1001 = 7x11x13,
215,441 = 17x19x23x29
and I think the next in the series should be
95,041,567 = 31x37x41x43x47.
47. 3 (The list is of the digits of pi/4)
48. pi^2 r^4 / 2 The hyper-volume of a 4-dimensional hyper-sphere.

[Christian Brøndum]

Post by j***@yahoo.com
If you spot an error or would like to add answers, please reply to this
post or send me an e-mail, or both.
Don't forget to explain your answer, the more detail the better.
http://www.eskimo.com/~miyaguch/titan.html
1. STRIP : MoBIUS :: BOTTLE : KLEIN
2. THOUGHT : ACTION :: OBSESSIVE : COMPULSIVE
3. LACKING MONEY : PENURIOUS :: DOTING ON ONE'S WIFE : UXORIOUS
(definitions)
4. MICE : MEN :: CABBAGES : KINGS (from literature)
5. TIRE : RETREAD :: PARCHMENT : PALIMPSEST
6. ALL IS ONE : MONISM :: ALL IS SELF : SOLIPSISM (a doctrine in
philosophy, nothing exists except the self, or alternately the
existence of everything else depends on the existence of the self)
7. SWORD : DAMOCLES :: BED : PROCRUSTES
8. THING : DANGEROUS :: SPRING : PIERIAN
(A little learning is a dangerous thing; drink deep, or taste not the
Pierian spring - Alexander Pope. An
Essay on Criticism)
9. HOLLOW VICTORY : PYRRHIC :: HOLLOW VILLAGE : Potemkin
10. PILLAR : OBELISK :: MONSTER : BASILISK (OBELISK from Greek
obeliskos, BASILISK from Greek basiliskos)
11. 4 : HAND :: 9 : SPAN (a hand is 4 inches, a span is 9 inches)
12. GOLD : MALLEABLE :: CHALK : FRIABLE (rhyming pattern)
13. EASY JOB : SINECURE :: GUIDING LIGHT : CYNOSURE (the rhyming
pattern is the key here)
14. LEG : AMBULATE :: ARM : BRACHIATE
15. MOSQUITO : MALARIA :: CANNIBALISM : KURU (a disease limited to the
Fore tribe of New Guinea, who eat human brain in their religious
rituals)
16. HEAR : SEE :: TEMPORAL : OCCIPITAL (Lobes of the brain that deal
with hearing and sight.
CLIOMETRICS (Cliometrics is the use of statistics or economics in
historical studies.)
18. JEKYLL : HYDE :: ELOI : MORLOCKS (from the books by Robert Louis
Stevenson and H.G. Wells)
19. UNIVERSE : COSMO- :: UNIVERSAL LAWS : COSMONOMOLOGO-
20. SET OF SETS NOT MEMBERS OF THEMSELVES : RUSSELL :: DARKNESS OF THE
NIGHT SKY IN AN INFINITE UNIVERSE : OLBERS
(KEPLER has also been offered as an answer)
21. TEACHING : UPLIFTING :: PEDAGOGIC : ANAGOGIC (from Greek
for spiritual uplift)
22. LANGUAGE GAMES : LUDWIG :: PIANO CONCERTI FOR THE LEFT HAND : PAUL
(So obscure it is silly. Ludwig and Paul Wittgenstein were brothers.
One was a pianist, the other was the famous philosopher who used the
phrase "language games" in his book Philosophical Investigations.
Knowing this meaningless bit of trivia can hardly be an indication of
great intelligence.)
23. IDOLS : TWILIGHT :: MORALS : GENEALOGY (Titles of Nietzsche's
books)
24. SWEET*NESS* : SUFFIX :: BOAT*SWAIN* : STEM ("ness" is a suffix,
"swain" is the stem of the compound word "boatswain."
Alternate answer is BASE, which fits the rhyming pattern better
29. The answer is 20.
31. The answer is 22
(this answer may be wrong)
37.
Initially, we need to consider 11 possibilities where we choose 10
white marbles.
1) After the insertion, the box contains 10 whites. The chances of
this are 1 in 2^10, i.e. 1 in 1024. If this is the case, in our
subsequent drawing we're bound to pick out 10 whites. Total probability
of this possibility = 1/1024
2) After the insertion, the box contains 9 whites. The chances of this
are 10!/9!/1! = 10 in 1024. If this is the case, in our subsequent
drawing our chances of picking out 10 whites is (9/10)^10 because we
have a 9/10 chance each time. Total probability of this possibility =
10/1024 * (9/10)^10
3) After the insertion, the box contains 8 whites. The chances of this
are 10!/8!/2! = 45 in 1024. If this is the case, in our subsequent
drawing our chances of picking out 10 whites is (8/10)^10 because we
have a 8/10 chance each time. Total probability of this possibility =
45/1024 * (8/10)^10
4) Box = 7 whites. Total = 120/1024 * (7/10)^10 i.e. nCr * (r/10)^10
5) Box = 6 whites. Total = 210/1024 * (6/10)^10
6) Box = 5 whites. Total = 252/1024 * (5/10)^10
7) Box = 4 whites. Total = 210/1024 * (4/10)^10
8 ) Box = 3 whites. Total = 120/1024 * (3/10)^10
9) Box = 2 whites. Total = 45/1024 * (2/10)^10
10) Box = 1 whites. Total = 10/1024 * (1/10)^10
11) Box = 0 whites. Total = 1/1024 * (0/10)^10 = 0!!
So, the chances of drawing 10 whites is the sum of these which is
0.013913029625. Approximately. However, we know that we actually drew
10 whites, so this 1 in 72 (ish) chance has happened. The chance that
it happened because we had possibility 1) above is the chance of 1)
relative to this 0.0139... chance. So, the answer is
(1/1024)/0.013913029625 which is 0.070190499... i.e. 7%.
So there!
I suggest that the answer you have given is to the question "What is
the probability of you pulling out 10 white marbles one at a time?"
The question is, however, "what is the probability of all marbles being
white(or black)? The answer to that, I believe, is 1/1024, which to
nearest % is '0'.
I just re-read it, and I think I got it right. The question is, what is
the probability of them all being white, given that you randomly
withdrew and returned 10 white marbles consecutively.
38. 2 / 27
39. 8 / 3^7 or 4 / 3^27 (two solutions have been offered)
http://groups.google.com/group/rec.puzzles/msg/8b1875e5406828ff?dmode=source
45. -4697
x = n^3 - n!
2^3 = 8, 2! = 2 so 8-2 = 6
3^3 = 27, 3! = 6 so 27-6 = 21
4^3 = 64, 4! = 24 so 64-24 = 40...
46. 95,041,567
the numbers are all products of increasingly large numbers of
successive primes.
2 = 2 (or 2x1?),
15 = 3x5,
1001 = 7x11x13,
215,441 = 17x19x23x29
and I think the next in the series should be
95,041,567 = 31x37x41x43x47.
47. 3 (The list is of the digits of pi/4)
48. pi^2 r^4 / 2 The hyper-volume of a 4-dimensional hyper-sphere.

[Stephen Young]

Post by j***@yahoo.com
If you spot an error or would like to add answers, please reply to this
post or send me an e-mail, or both.
Don't forget to explain your answer, the more detail the better.
http://www.eskimo.com/~miyaguch/titan.html
1. STRIP : MoBIUS :: BOTTLE : KLEIN
2. THOUGHT : ACTION :: OBSESSIVE : COMPULSIVE
3. LACKING MONEY : PENURIOUS :: DOTING ON ONE'S WIFE : UXORIOUS
(definitions)
4. MICE : MEN :: CABBAGES : KINGS (from literature)
5. TIRE : RETREAD :: PARCHMENT : PALIMPSEST
6. ALL IS ONE : MONISM :: ALL IS SELF : SOLIPSISM (a doctrine in
philosophy, nothing exists except the self, or alternately the
existence of everything else depends on the existence of the self)
7. SWORD : DAMOCLES :: BED : PROCRUSTES
8. THING : DANGEROUS :: SPRING : PIERIAN
(A little learning is a dangerous thing; drink deep, or taste not the
Pierian spring - Alexander Pope. An
Essay on Criticism)
9. HOLLOW VICTORY : PYRRHIC :: HOLLOW VILLAGE : Potemkin
10. PILLAR : OBELISK :: MONSTER : BASILISK (OBELISK from Greek
obeliskos, BASILISK from Greek basiliskos)
11. 4 : HAND :: 9 : SPAN (a hand is 4 inches, a span is 9 inches)
12. GOLD : MALLEABLE :: CHALK : FRIABLE (rhyming pattern)
13. EASY JOB : SINECURE :: GUIDING LIGHT : CYNOSURE (the rhyming
pattern is the key here)
14. LEG : AMBULATE :: ARM : BRACHIATE
15. MOSQUITO : MALARIA :: CANNIBALISM : KURU (a disease limited to the
Fore tribe of New Guinea, who eat human brain in their religious
rituals)
16. HEAR : SEE :: TEMPORAL : OCCIPITAL (Lobes of the brain that deal
with hearing and sight.
CLIOMETRICS (Cliometrics is the use of statistics or economics in
historical studies.)
18. JEKYLL : HYDE :: ELOI : MORLOCKS (from the books by Robert Louis
Stevenson and H.G. Wells)
19. UNIVERSE : COSMO- :: UNIVERSAL LAWS : COSMONOMOLOGO-
20. SET OF SETS NOT MEMBERS OF THEMSELVES : RUSSELL :: DARKNESS OF THE
NIGHT SKY IN AN INFINITE UNIVERSE : OLBERS
(KEPLER has also been offered as an answer)
21. TEACHING : UPLIFTING :: PEDAGOGIC : ANAGOGIC (from Greek
for spiritual uplift)
22. LANGUAGE GAMES : LUDWIG :: PIANO CONCERTI FOR THE LEFT HAND : PAUL
(So obscure it is silly. Ludwig and Paul Wittgenstein were brothers.
One was a pianist, the other was the famous philosopher who used the
phrase "language games" in his book Philosophical Investigations.
Knowing this meaningless bit of trivia can hardly be an indication of
great intelligence.)
23. IDOLS : TWILIGHT :: MORALS : GENEALOGY (Titles of Nietzsche's
books)
24. SWEET*NESS* : SUFFIX :: BOAT*SWAIN* : STEM ("ness" is a suffix,
"swain" is the stem of the compound word "boatswain."
Alternate answer is BASE, which fits the rhyming pattern better
29. The answer is 20.
31. The answer is 22
(this answer may be wrong)
37.
Initially, we need to consider 11 possibilities where we choose 10
white marbles.
1) After the insertion, the box contains 10 whites. The chances of
this are 1 in 2^10, i.e. 1 in 1024. If this is the case, in our
subsequent drawing we're bound to pick out 10 whites. Total probability
of this possibility = 1/1024
2) After the insertion, the box contains 9 whites. The chances of this
are 10!/9!/1! = 10 in 1024. If this is the case, in our subsequent
drawing our chances of picking out 10 whites is (9/10)^10 because we
have a 9/10 chance each time. Total probability of this possibility =
10/1024 * (9/10)^10
3) After the insertion, the box contains 8 whites. The chances of this
are 10!/8!/2! = 45 in 1024. If this is the case, in our subsequent
drawing our chances of picking out 10 whites is (8/10)^10 because we
have a 8/10 chance each time. Total probability of this possibility =
45/1024 * (8/10)^10
4) Box = 7 whites. Total = 120/1024 * (7/10)^10 i.e. nCr * (r/10)^10
5) Box = 6 whites. Total = 210/1024 * (6/10)^10
6) Box = 5 whites. Total = 252/1024 * (5/10)^10
7) Box = 4 whites. Total = 210/1024 * (4/10)^10
8 ) Box = 3 whites. Total = 120/1024 * (3/10)^10
9) Box = 2 whites. Total = 45/1024 * (2/10)^10
10) Box = 1 whites. Total = 10/1024 * (1/10)^10
11) Box = 0 whites. Total = 1/1024 * (0/10)^10 = 0!!
So, the chances of drawing 10 whites is the sum of these which is
0.013913029625. Approximately. However, we know that we actually drew
10 whites, so this 1 in 72 (ish) chance has happened. The chance that
it happened because we had possibility 1) above is the chance of 1)
relative to this 0.0139... chance. So, the answer is
(1/1024)/0.013913029625 which is 0.070190499... i.e. 7%.
So there!
I suggest that the answer you have given is to the question "What is
the probability of you pulling out 10 white marbles one at a time?"
The question is, however, "what is the probability of all marbles being
white(or black)? The answer to that, I believe, is 1/1024, which to
nearest % is '0'.
I just re-read it, and I think I got it right. The question is, what is
the probability of them all being white, given that you randomly
withdrew and returned 10 white marbles consecutively.
38. 2 / 27
39. 8 / 3^7 or 4 / 3^27 (two solutions have been offered)
http://groups.google.com/group/rec.puzzles/msg/8b1875e5406828ff?dmode=source
45. -4697
x = n^3 - n!
2^3 = 8, 2! = 2 so 8-2 = 6
3^3 = 27, 3! = 6 so 27-6 = 21
4^3 = 64, 4! = 24 so 64-24 = 40...
46. 95,041,567
the numbers are all products of increasingly large numbers of
successive primes.
2 = 2 (or 2x1?),
15 = 3x5,
1001 = 7x11x13,
215,441 = 17x19x23x29
and I think the next in the series should be
95,041,567 = 31x37x41x43x47.
47. 3 (The list is of the digits of pi/4)
48. pi^2 r^4 / 2 The hyper-volume of a 4-dimensional hyper-sphere.

Does anyone know of a similar conversation about the Langdon Adult Intelligence Test? I came across it in an old magazine and took it, but it is no longer scored.