N balls with numbers 1,2,3...N are filled arbitrarily into 3 urns A,B and C - but no urn may remain empty. We write P(A,B) for the probability that a ball chosen randomly from urn A shows a higher number than a ball chosen randomly from urn B. We call the tree urns intransitive if P(A,B)>1/2, P(B,C)

Imagine that you are given a box with n nuts and n screws. Each screw have different size (diameter) and on each screw there is exactly one matching nut that fits. How many tries on average do you need to assign each nut to a particular screw? (Try to minimize tries as much as possible) The only ...

376 is a magic number! When we raise it to some integer power then the result always ends in 376: $376^2 = 141376$ $376^3 = 53157376$ $376^4 = 19987173376$ $376^5 = 7515177189376$ $376^6 = 2825706623205376$ $376^7 = 1062465690325221376$ ... Why is this so? Can you find another 3-digit number with...

You are given three meter scales A, B, and C are shown in picture given below. The scales are however, quite unique in their properties as they have different numbers of division per meter. You are asked to measure the length of the rod using the scales given to you. What is the range of the leng...

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