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 Amazing: Stefan Glock, Daniela Kühn, Allan Lo, and Deryk Osthus give a new proof for Keevash’s Theorem. And more news on designs.
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 Polymath 10 post 6: The ErdosRado sunflower conjecture, and the Turan (4,3) problem: homological approaches.
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Tag Archives: Test your intuition
Itai Ashlagi, Yashodhan Kanoria, and Jacob Leshno: What a Difference an Additional Man makes?
We are considering the stable marriage theorem. Suppose that there are n men and n women. If the preferences are random and men are proposing, what is the likely average women’s rank of their husbands, and what is the likely average … Continue reading
Test Your Intuition (19): The Advantage of the Proposers in the Stable Matching Algorithm
Stable mariage The GaleShapley stable matching theorem and the algorithm. GALESHAPLEY THEOREM Consider a society of n men and n women and suppose that every man [and every woman] have a preference (linear) relation on the women [men] he [she] knows. Then … Continue reading
Test Your Intuition (17): What does it Take to Win TicTacToe
(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
Discrepancy, The BeckFiala 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
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
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
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 Mathoverflow, Test your intuition
6 Comments
Test Your Intuition (12): Perturbing a Polytope
Let P be a ddimensional 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 Convex polytopes, Test your intuition
4 Comments
Test Your Intuition (11): Is it Rational to Insure a Toaster
Here is a question from last year’s exam in the course “Basic Ideas of Mathematics”: You buy a toaster for 200 NIS ($50) and you are offered one year of insurance for 24 NIS ($6). a) Is it … Continue reading
Posted in Probability, Rationality, Teaching, Test your intuition
Tagged Insurance, Test your intuition
18 Comments
Test Your Intuition (10): How Does “Random Noise” Look
This is a bit unusual post in the “test your intuition” corner as the problem is not entirely formal. How does random noise in the digital world typically look? Suppose you have a memory of n bits, or a memory based on a larger … Continue reading