Category Archives: Test your intuition

Stan Wagon, TYI 23: Ladies and Gentlemen: The Answer

TYI 32, kindly offered by Stan Wagon asked A round cake has icing on the top but not the bottom. Cut out a piece in the usual shape (a sector of a circle with vertex at the center), remove it, … Continue reading

Posted in Combinatorics, Geometry, Test your intuition | Tagged , | 8 Comments

TYI 31 – Rados Radoicic’s Rope Problem

  Ropemaker (source) Rados Radoicic wrote me: “Several years back, I heard the following puzzle that turns out to be rather ‘classical’: “There are N ropes in a bag. In each step, two rope ends are picked uniformly at random, tied … Continue reading

Posted in Combinatorics, Probability, Test your intuition | Tagged , | 7 Comments

Elchanan Mossel’s Amazing Dice Paradox (your answers to TYI 30)

TYI 30 asked Elchanan Mossel’s Amazing Dice Paradox (that I heard from Yuval Peres yesterday) You throw a die until you get 6. What is the expected number of throws (including the throw giving 6) conditioned on the event that all throws … Continue reading

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TYI 30: Expected number of Dice throws

Test your intuition: You throw a dice until you get 6. What is the expected number of throws (including the throw giving 6) conditioned on the event that all throws gave even numbers. follow-up post

Posted in Combinatorics, Probability, Test your intuition | Tagged | 37 Comments

Test your intuition 29: Diameter of various random trees

Both trees in general and random trees in particular are wonderful objects. And there is nothing more appropriate to celebrate Russ Lyons great birthday conference “Elegance in Probability” (taking place now in Tel Aviv) than to test your intuition, dear … Continue reading

Posted in Combinatorics, Probability, Test your intuition | Tagged , | 19 Comments

Test your intuition 28: What is the most striking common feature to all these remarkable individuals

Test your intuition: What is the most striking common feature to all these fifteen remarkable individuals László Babai; Avi Wigderson; Lance Fortnow; Lane Hemaspaandra; Sampath Kannan; Hal Gabow; Richard Karp; Tom Leighton; Rockford J. Ross; Alan Selman; Michael Langston; S. … Continue reading

Posted in Computer Science and Optimization, Test your intuition | 1 Comment

Test Your Intuition (27) about the Alon-Tarsi Conjecture

On the occasion of Polymath 12 devoted to the Rota basis conjecture let me remind you about the Alon-Tarsi conjecture and test your intuition concerning a strong form of the conjecture. The sign of a Latin square is the product … Continue reading

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TYI 26: Attaining the Maximum

(Thanks, Dani!) Given a random sequence , ******, , let . and assume that .  What is the probability that the maximum value of is attained only for a single value of ? Test your intuition: is this probability bounded … Continue reading

Posted in Combinatorics, Probability, Test your intuition | Tagged | 21 Comments

TYI 25: The Automorphism Group of the Symmetric Group

True or False: The group of automorphisms of the symmetric group , n ≥ 3 is itself.  

Posted in Algebra and Number Theory, Test your intuition | Tagged , | 7 Comments

Test your intuition 24: Which of the following three groups is trivial

Martin Bridson We have three finitely presented groups A is generated by two generators a and b and one relation   B is generated by three generators a, b, c and three relations ,    . C is generated by four generators a, b, c, d … Continue reading

Posted in Algebra and Number Theory, Test your intuition | Tagged , | 10 Comments