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.
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.
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.
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.
[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.
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.
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.
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
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
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
--
Disclaimer: I am in no way responsible for any of the statements
made in the above text. For all I know I might be
drugged or something..
No I'm not paranoid. You all think I'm paranoid, don't you !
#EOT
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.
>Puppet_Sock wrote:
>) judgero...@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.
>
Sure, but there's a LOT of those "only ones".
Do nihilsts believe in nihilsm?
Socks
I'm a solipsist-by-proxy. Same as solipsism, except it's someone
else's self which exists.
--
There's no such thing as a free lunch, but certain accounting practices can
result in a fully-depreciated one.
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."
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.
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.
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.
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?
>
> 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".
> 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.
>
> 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.
12 consecutive posts without a single reply.
Feeding doesn't appear to be an issue, does it?
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.
> > 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).
> > > 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 : ???
>
> 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.
It's not a real word. I made it up. I can assign any meaning to it
I choose. Duh.
> >
> > 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?
> > (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?
> ... 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?
> 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.
> 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.
It would if the darts champion thinks that being good at darts
means he should be good at snooker.
>
> 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.
> > 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?
<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>
> 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.