Category Archives: Test your intuition

Some News from a Seminar in Cambridge

On an old problems of Erdős (h/t Michael Simkin and Nati Linial) Here is a somewhat mysterious announcement for a combinatorics seminar lecture at Cambridge. Which old problems of Erdős are we talking about? Here is a picture from the … Continue reading

Posted in Combinatorics, Test your intuition | Tagged , , , , | 9 Comments

Barnabás Janzer: Rotation inside convex Kakeya sets

Barnabás Janzer studied the following question: Suppose we have convex body in that contains a copy of a convex body in every orientation. Is it always possible to move any one copy of to another copy of , keeping inside … Continue reading

Posted in Convexity, Test your intuition | Tagged , | 1 Comment

Test Your intuition 51

Suppose that and are two compact convex sets in space. Suppose that contains . Now consider two quantities is the average volume of a simplex forms by four points in drawn uniformly at random. is the average volume of a … Continue reading

Posted in Convexity, Geometry, Probability, Test your intuition | Tagged | 12 Comments

Answer to Test Your Intuition 50: Detecting a Deviator

Two weeks ago we asked: Ruth and Ron start together at the origin and take a walk on the integers. Every day they make a move. They take turns in flipping a coin and they move together right or left … Continue reading

Posted in Games, Probability, Test your intuition | Tagged | 8 Comments

Test Your Intuition 50. Two-Player Random Walk; Can You Detect Who Did Not Follow the Rules?

Ruth and Ron start together at the origin and take a walk on the integers. Every day they make a move. They take turns in flipping a coin and they move together right or left according to the outcome. Their … Continue reading

Posted in Probability, Test your intuition | Tagged , | 13 Comments

Ehud Friedgut: How many cubes of 2×2×2 fit into a box of size 8×4×3? (TYI 49)

This blog post is kindly written by Ehud Friedgut. My daughter, Shiri, who’s in seventh grade, had the following question in a math exam: How many cubes of 2×2×2 fit into a box of size 8×4×3? Shiri divided the volumes, … Continue reading

Posted in Geometry, Riddles, Test your intuition | Tagged , , , | 6 Comments

To cheer you up in difficult times 35 combined with Test Your Intuition 48: Alef’s corner – Jazz and Math

Test your intuition: What is the true title of this drawing?

Posted in Art, Music, Test your intuition, What is Mathematics | Tagged , | 1 Comment

Test your intuition 47: AGC-GTC-TGC-GTC-TGC-GAC-GATC-? what comes next in the sequence?

Before getting to the main topic of this post, first, Happy New Year 2022 and Merry Christmas to all readers, and second, a quick update: A community blog to discuss open problems in algebraic combinatorics was created. Everybody is invited … Continue reading

Posted in Algebra, Combinatorics, Geometry, Test your intuition | Tagged , | 1 Comment

Test Your Intuition (46): What is the Reason for Maine’s Huge Influence?

Very quick updates: Corona: Israel is struggling with the pandemic with some successes,  some failures, and much debate. Peace: We have peace agreements now with several Arab countries, most recently with Sudan. This is quite stunning. Internal politics: As divided … Continue reading

Posted in Games, Probability, Statistics, Test your intuition | Tagged , | 6 Comments

Cheerful Test Your Intuition (#45): Survey About Sisters and Brothers

You survey many many school children and ask each one: Do you have more brothers than sisters? or more sisters than brothers? or the same number? Then you separate the boys’s answers from the girls’s answers Which of the following … Continue reading

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