(related to Problem: The Dissected Triangle)

Diagram $A$ is our original triangle. We will say it measures $5$ inches (or $5$ feet) on each side. If we take off a slice at the bottom of an equilateral triangle by a cut parallel with the base, the portion that remains will always be an equilateral triangle; so we first cut off piece $1$ and get a triangle $3$ inches on every side. The manner of finding directions of the other cuts in $A$ is obvious from the diagram.


Now, if we want two triangles, $1$ will be one of them, and $2,$ $3,$ $4,$ and $5$ will fit together, as in $B,$ to form the other. If we want three equilateral triangles, $1$ will be one, $4$ and $5$ will form the second, as in $C,$ and $2$ and $3$ will form the third, as in $D.$ In $B$ and $C$ the piece $5$ is turned over; but there can be no objection to this, as it is not forbidden, and is in no way opposed to the nature of the puzzle.

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Project Gutenberg

  1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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