# Puzzle of the Week for 1 June 1999

Take a piece of paper in the shape of an equilateral triangle, and cut it
so that all of the pieces are also equilateral triangles. It's not possible
to cut the original triangle into only two or three such pieces, but four
equilateral triangles can be obtained from one without much difficulty.

What is the *largest* number of equilateral triangles that
*cannot* be obtained in this way? (Assume that you may cut the
triangles as small as you wish.)

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