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 any
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.
[Illustration]