Tag Archives: Test your intuition

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

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 , | 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

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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

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

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

Posted in Convexity, Probability, Test your intuition | Tagged | 5 Comments

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

Posted in Convexity, Test your intuition | Tagged | 14 Comments

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

Posted in Probability, Test your intuition | Tagged | 26 Comments

Test Your Intuition (6)

This is not as clear cut a question as the earlier ones, and if you do not know an answer then it will be difficult to figure one out just based on intuition. (But perhaps possible). If you are intrigued by … Continue reading

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Test Your Intuition (5)

  (Not such a set) consider a planar set A with the following property. In every direction, the distance between the two parallel lines that touch A from both sides is the same! Must A be a circle?

Posted in Convexity, Test your intuition | Tagged | 4 Comments