Monthly Archives: November 2010

Five groups

Mathematicians are divided into five groups: those who can count to 2, those who can count to 3, those who can count to 4 and logicians.

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Splitting A Rectangle

Find all ways to cut a rectangle into two connected pieces of equal area so that they can be rearranged to get a new rectangle with different dimensions (side lengths) than the orgininal one. I already know countably many ways. … Continue reading

Posted in Geometry, Mathematics, Recreation, Wednesday Problem | 2 Comments


Pick randomly three points on the unit sphere. The geodesic triangle with these points as vertices divides the sphere into two parts. What is the probability that the north pole is contained in the smaller of these parts? For instance … Continue reading

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Can Mathematics Solve Philosophical Problems?

This post is not an attempt to answer the question of the subject, but merely to discuss related topics. The idea dates back to the time when I first learned what is the likelihood function in probability theory. When one … Continue reading

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A Year Problem

There are more year problems than years. But since I have been pondering on this particular one, I will present it here. You are allowed to use +, -, / and * (plus, minus, division and multiplication) signs and bracketing. … Continue reading

Posted in Algebra, Combinatorics, Mathematics, Recreation, Wednesday Problem | 12 Comments