http://www.eskimo.com/~miyaguch/titan.html
I found this while looking into Marilyn vos Savant's background in
this thread.
They say that only 1 in a million people can get 90% of them right, or 43 of 48 questions. That's what it takes to get in the Mega Society. Some other high IQ societies only require you to get 50% right, and you'd still be way above Mensa level. That's how hard it is.
A few of the questions:
VERBAL ANALOGIES
Write the word or prefix that best completes each analogy. For example, in the analogy MAN : WOMAN :: ANDRO- : ?, the best answer would be GYNO-.
1. STRIP : MÖBIUS :: BOTTLE : ?
10. PILLAR : OBELISK :: MONSTER : ?
22. LANGUAGE GAMES : LUDWIG :: PIANO CONCERTI FOR THE LEFT HAND : ?
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SPATIAL PROBLEMS
The design to the right is made up of three squares of different sizes, lying one on top of another.
What is the minimum number of squares that would be sufficient to create each of the following patterns?
26.
27.
29. Suppose 27 identical cubes are glued together to form a cubical stack as illustrated to the right. If one of the small cubes is omitted, four distinct shapes are possible; one in which the omitted cube is at a corner of the stack, one in which it is at the middle of an edge of the stack, one in which it is at the middle of a side of the stack, and one in which it is at the core of the stack. If two of the small cubes are omitted rather than just one, how many distinct shapes are possible?
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INTERPENETRATIONS
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?
35. Suppose two right circular cones and one right circular cylinder mutually interpenetrate, with the base of each cone and both bases (i.e., both ends) of the cylinder sealed by precisely fitting flat circular surfaces. What is the maximum number of pieces (i.e., completely bounded volumes) that can thus be formed, considering only the surfaces of these three figures as boundaries and counting only pieces that are not further subdivided?
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PROBABILITIES
37. Suppose you are truthfully told that ten marbles were inserted into a box, all of them identical except that their colors were determined by the toss of an unbiased coin. When heads came up, a white marble was inserted, and when tails came up, a black one. You reach into the box, draw out a marble, inspect its color, then return it to the box. You shake the box to mix the marbles randomly, and then reach in and again select a marble at random. If you inspect ten marbles in succession in this manner and all turn out to be white, what is the probability to the nearest whole percent that all ten marbles in the box are white?
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Suppose there is an ant at each vertex of a triangle and the three ants simultaneously crawl along a side to the next vertex. The probability that no two ants will encounter one another is 2/8, since the only two cases in which no encounter occurs are when the ants all go left (clockwise) -- LLL -- or all go right (counterclockwise) -- RRR. In the six other cases -- RRL, RLR, RLL, LLR, LRL, and LRR -- there will be an encounter.
For the following five problems, imagine there is an ant at each vertex and that the ants all simultaneously crawl along an edge to the next vertex, each ant choosing its path randomly. What is the probability that no ant will encounter another, either en route or at the next vertex, for each of the following regular polyhedrons? (Express your answer as a reduced fraction; e.g., 2/8 = 1/4.)
38. A tetrahedron
39. A cube
40. An octahedron
41. A dodecahedron
42. An icosahedron
NUMBER SEQUENCES
Determine the value of ___ in each of the following sequences. For example, in the sequence
1 4 9 16 25 ___ 49 64, the value of ___ is 36.
43. 4/10 ___/100 168/1,000 1,229/10,000 9,592/100,000 78,498/1,000,000
44. 1 4 17 54 145 368 945 ___
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48.