**The Titan Test**

Even harder than the Mega!

Published online with permission from the author:

Ronald K. Hoeflin

P.O. Box 539

New York, NY 10101

Send questions/comments related to this Web page to Darryl Miyaguchi

Changes:

04/12/03 | Scoring fee lowered from $30 to $25. |

09/24/01 | Scoring fee increased from $20 to $30. |

04/05/01 | Scoring fee reduced to $20. |

01/04/00 | Scoring fee increased from $25 to $33. |

12/27/97 | Problem 33 again (my bad). The wording of the addendum should read, "Each of the Möbius strips..." rather than "The Möbius strip..." |

6/22/97 | Added cross-references to the Hoeflin Power Test where appropriate. |

6/8/97 | Reverted back to the drawings of dodecahedra and icosahedra that Hoeflin uses, which may be clearer. |

6/7/97 | Incorporated response from Ron regarding reference material. |

6/2/97 | Problem 33 of the Titan Test has been
altered since its publication in Omni Magazine.
The problem in its Omni version is virtually
unsolvable. My guess is that people who have already
submitted Titan Test answer sheets will not be able
resubmit the answer to this one modified problem -- doing
so would allow one to determine whether or not he or she
answered that problem correctly. |

6/2/97 | The rule regarding use of pocket calculators has been clarified. A question has been asked about the fairness of using the full search capabilities of current online library catalogs to help solve analogies. I am awaiting a ruling from Ron. |

6/2/97 | Subscores to the tests are no longer reported. |

INSTRUCTIONS:

1. ANSWER SHEET. Please print out the answer sheet and write your answers there. Provide the other information requested too.

2. TIME LIMIT. There is no enforceable time limit, but one month would be a reasonable amount of time to spend on the test.

3. ADDITIONS AND CORRECTIONS TO ANSWERS: No additions or corrections to your initial set of answers will be accepted. You get only one try at this test, so do your best the first time.

4. ASSISTANCE. So that no one will gain an unfair advantage by using reference aids, everyone is both permitted and encouraged to use books (In response to the question of online library catalog searches, Hoeflin writes: "I'd prefer that people employ just a dictionary and thesaurus in book form ... my test is not intended to be a test of computer-using skills."). Paper and pencil should suffice for this test, but if desired, you may use a non-programmable pocket calculator (for addition, subtraction, multiplication, or division); however, computers are not allowed as aids to the test. This restriction includes, but is not limited to the use of: commercial offerings such as spreadsheets and mathematical programs, user-written programs, electronic encyclopedias, Web search engines, and online sequence databases. Any assistance from other persons is prohibited.

If you have plans to take Hoeflin's Power Test (a compilation of the best nonverbal and non-sequence problems from the Mega, Titan, and Ultra Tests), you should be aware that that test has more restrictive rules, disallowing the use of calculators and reference material altogether. I have provided cross-references to the Power Test -- you are free to use or ignore these links as appropriate for you. [DTM]

5. DISCUSSION OF PROBLEMS. As the Titan Test may be used as an admissions test to several societies, please do not share answers in a public forum with anyone who has not tried this test already. If you have plans to take Hoeflin's Power Test, then you should not share answers at all.

6. GUESSING. There is no penalty for wrong answers or guesses, so it is to your advantage to guess whenever you are unsure of an answer.

7. FEE. There is $25 scoring fee, payable to the test designer, "Ronald K. Hoeflin," at P.O. Box 539, New York, NY 10101, U.S.A. Checks or money orders must be made payable in U.S. dollars through any U.S. bank or post office. Please remember that postal delivery services which require a signature cannot be delivered to post office boxes. You will receive a scoresheet showing your raw score, your corresponding I.Q. score, and its estimated percentile in the general population. Subscores within the test are no longer reported because it gives people too much of a clue which problems they got right or wrong and because the subtests are too short to be much help to people in evaluating their verbal or math aptitudes.

8. SCORESHEETS. Send to Ronald K. Hoeflin at the above address. Allow up to four weeks to elapse before complaining about not receiving a score report. Most scores are sent out within two or three weeks of the receipt of your answers.

8. SOCIETY ADMISSIONS USAGE: This test is accepted as an admissions test by the Top One Percent Society (minimum: 10 right), the One-in-a-Thousand Society (24 right), the IQuadrivium Society (24 right), the Glia Society (24 right), the Prometheus Society (36 right, obtained before April 25, 1999), and the Mega Society (43 right).

**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 : ?

2. THOUGHT : ACTION :: OBSESSIVE : ?

3. LACKING MONEY : PENURIOUS :: DOTING ON ONE'S WIFE : ?

4. MICE : MEN :: CABBAGES : ?

5. TIRE : RETREAD :: PARCHMENT : ?

6. ALL IS ONE : MONISM :: ALL IS SELF : ?

7. SWORD : DAMOCLES :: BED : ?

8. THING : DANGEROUS :: SPRING : ?

9. HOLLOW VICTORY : PYRRHIC :: HOLLOW VILLAGE : ?

10. PILLAR : OBELISK :: MONSTER : ?

11. 4 : HAND :: 9 : ?

12. GOLD : MALLEABLE :: CHALK : ?

13. EASY JOB : SINECURE :: GUIDING LIGHT : ?

14. LEG : AMBULATE :: ARM : ?

15. MOSQUITO : MALARIA :: CANNIBALISM : ?

16. HEAR : SEE :: TEMPORAL : ?

17. ASTRONOMY AND PHYSICS : ASTROPHYSICS :: HISTORY AND
STATISTICS : ?

18. JEKYLL : HYDE :: ELOI : ?

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

20. SET OF SETS NOT MEMBERS OF THEMSELVES : RUSSELL :: DARKNESS
OF THE NIGHT SKY IN AN INFINITE UNIVERSE : ?

21. TEACHING : UPLIFTING :: PEDAGOGIC : ?

22. LANGUAGE GAMES : LUDWIG :: PIANO CONCERTI FOR THE LEFT HAND :
?

23. IDOLS : TWILIGHT :: MORALS : ?

24. SWEET*NESS* : SUFFIX :: BOAT*SWAIN* : ?

**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? |

25. | [cf. Hoeflin Power Test, problem 2] |

26. |

27. |

28. | If each side of a tetrahedron is an equilateral triangle painted white or black, five distinct patterns are possible: all sides white, all black, just one side white, just one black, and two sides white and two black. If each side of an octahedron is a white or black equilateral triangle, how many distinct patterns are possible? [cf. Hoeflin Power Test, problem 7] |

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? [cf. Hoeflin Power Test, problem 19] |

30. | Suppose a diagonal is drawn across each side of a cube from one corner to the other (see illustration to the right). How many distinct patterns are possible, considering all possible orientations of the diagonals, including all six sides of the cube in each pattern? [cf. Hoeflin Power Test, problem 29] |

**SLICE AND DICE**

31. | A perfectly spherical onion is sliced by six perfectly straight knife strokes; the pieces thereby formed never having been moved from their original positions. What is the maximum number of pieces into which the infinitesimally thin outer skin of the onion can thus be divided? [cf. Hoeflin Power Test, problem 10] |

32. | A tetrahedral lump of clay is sliced by six perfectly straight cuts, the pieces never moving from their original positions. What is the maximum number of tetrahedral pieces that can thus be formed, counting only pieces that are not further subdivided? [cf. Hoeflin Power Test, problem 11] |

33. | Consider the torus, a doughnut-shaped
solid that is perfectly circular at each perpendicular
cross section, and a Möbius strip, which has a single
180-degree twist and a uniform curvature throughout its
length. Suppose a torus is sliced three times by 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? Note: Each of the Möbius strips is entirely confined to the interior of the torus. [cf. Hoeflin Power Test, problem 13] |

**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? [cf. Hoeflin Power Test, problem 4] |

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? [cf. Hoeflin Power Test, problem 27] |

36. | If a cube and a tetrahedron interpenetrate, what is the maximum possible number of solid pieces (i.e., completely bounded volumes not further subdivided)? [cf. Hoeflin Power Test, problem 25] |

**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? [cf. Hoeflin Power Test, problem 31] |

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 [cf. Hoeflin Power Test, problem 21] |

39. | A cube [cf. Hoeflin Power Test, problem 22] |

40. | An octahedron [cf. Hoeflin Power Test, problem 23] |

41. | A dodecahedron (illustrated to the right) [cf. Hoeflin Power Test, problem 24] |

42. | An icosahedron (illustrated to the right) |

**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 ___

45. 0 6 21 40 5 -504 ___

46. 2 15 1,001 215,441 ___

47. 7 8 5 3 9 8 1 6 3 ___

48. |

This concludes the test.

Look at the Titan Test Norming

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