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Haberdasher Problem

A geometric figure with n sides can be divided into pieces that, when rearranged, can form a geometric figure with m sides. This works for any integer values of m and n — that is, any polygon can be divided into pieces that will form a different polygon. For instance, four cuts will divide a regular octagon into five pieces that can be rearranged to form a square, as shown below.

The Haberdasher problem is the most famous problem of this type. (And its solution is arguably one of the most beautiful results in mathematics.) First proposed by puzzler Henry Ernest Dudeney in 1907, it can be stated as follows:

With just three cuts, divide an equilateral triangle into
pieces that can be rearranged to form a square.

But beware! Although the problem can be stated simply, its solution is not simple to find!

Henry Ernest Dudeney

Henry Ernest Dudeney was an author and mathematician. Known as one of England's foremost puzzle creators, he authored six books of puzzles.

The following quote by Dudeney implies that problem-solving ability relies more on persistence and creativity than education:

Many of the best problems cannot be solved by any familiar scholastic methods, but must be attacked on entirely original lines.

Two of Dudeney's books (without illustrations) can be downloaded for free from ManyBooks: