Category Archives: Test your intuition

Mittag-Leffler Institute and Yale, Winter 2005; Test your intuition: Who Played the Piano?

This is a little “flashback” intermission in my posts about my debate with Aram Harrow. This time I try to refer to Cris Moore’s question regarding  the motivation for my study. For the readers it gives an opportunity to win a … Continue reading

Posted in Computer Science and Optimization, Controversies and debates, Physics, Test your intuition | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | 9 Comments

Test Your Intuition (17): What does it Take to Win Tic-Tac-Toe

(A few more quantum posts are coming. But let’s have a quick break for games.) Tic Tac Toe is played since anciant times. For the common version, where the two players X and O take turns in marking the empty squares … Continue reading

Posted in Games, Test your intuition | Tagged , , | 40 Comments

What does “beyond a reasonable doubt” practically mean?

(Motivated by two questions from Gowers’s How should mathematics be taught to non mathematicians.)

Posted in Law, Probability, Test your intuition | 18 Comments

Test Your Intuition (16): Euclid’s Number Theory Theorems

Euclid’s Euclid’s book IX on number theory contains 36 propositions. The 36th proposition is: Proposition 36.If as many numbers as we please beginning from a unit are set out continuously in double proportion until the sum of all becomes prime, … Continue reading

Posted in Algebra and Number Theory, Test your intuition | Tagged , | 16 Comments

Test Your Intuition (15): Which Experiment is More Convincing

Consider the following  two scenarios (1) An experiment tests the effect of a new medicine on people which have a certain illness. The conclusion of the experiment is that for 5% of the people tested the medication led to improvement while for … Continue reading

Posted in Statistics, Test your intuition | 19 Comments

Discrepancy, The Beck-Fiala Theorem, and the Answer to “Test Your Intuition (14)”

The Question Suppose that you want to send a message so that it will reach all vertices of the discrete -dimensional cube. At each time unit (or round) you can send the message to one vertex. When a vertex gets the … Continue reading

Posted in Combinatorics, Test your intuition | Tagged , | 6 Comments

Test Your Intuition (14): A Discrete Transmission Problem

Recall that the -dimensional discrete cube is the set of all binary vectors ( vectors) of length n. We say that two binary vectors are adjacent if they differ in precisely one coordinate. (In other words, their Hamming distance is 1.) This … Continue reading

Posted in Combinatorics, Test your intuition | Tagged | 35 Comments

Test Your Intuition (13): How to Play a Biased “Matching Pennies” Game

Recall the game “matching pennies“. Player I has to chose between ’0′ or ’1′, player II has to chose between ’0′ and ’1′.No player knows what is the choice of the other player before making his choice. Player II pays … Continue reading

Posted in Games, Test your intuition | Tagged | 5 Comments

False Beliefs in Mathematics

Test your intuition: For two n by n matrices A and B, is it always the case that tr(ABAB) = tr(ABBA)?

Posted in Mathematics over the Internet, Test your intuition | Tagged , | 6 Comments

Test Your Intuition (12): Perturbing a Polytope

Let P be a d-dimensional convex polytope. Can we always perturb the vertices of P moving them to points with rational coordinates without changing the combinatorial structure of P? In order words, you require that a set of vertices whose … Continue reading

Posted in Convex polytopes, Test your intuition | Tagged , | 4 Comments