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# Category Archives: Test your intuition

## 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 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 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

## Answer to Test Your Intuition (9)

Two experimental results of 10/100 and 15/100 are not equivalent to one experiment with outcomes 3/200. (Here is a link to the original post.) One way to see it is to think about 100 experiments. The outcomes under the null … Continue reading

## Buffon’s Needle and the Perimeter of Planar Sets of Constant Width

Here is an answer to “Test your intuition (8)”. (Essentially the answer posed by David Eppstein.) (From Wolfram Mathworld) Buffon’s needle problem asks to find the probability that a needle of length will land on a line, given a floor … Continue reading

## Test Your Intuition (8)

Consider all planar sets A with constant width 1. Namely, in every direction, the distance between the two parallel lines that touch A from both sides is 1. We already know that there exists such sets other than the circle … Continue reading

## Test Your Intuition (7)

Consider the following game: you have a box that contains one white ball and one black ball. You choose a ball at random and then return it to the box. If you chose a white ball then a white ball is added to … Continue reading