nditions ought to be easily understood, or people will not attempt
a solution.

If the reader were now asked "to cut a half-square into as few pieces as
possible to form a Greek cross," he would probably produce our solution,
Figs. 31-32, and confidently claim that he had solved the puzzle
correctly. In this way he would be wrong, because it is not now stated
that the square is to be divided diagonally. Although we should always
observe the exact conditions of a puzzle we must not read into it
conditions that are not there. Many puzzles are based entirely on the
tendency that people have to do this.

The very first essential in solving a puzzle is to be sure that you
understand the exact conditions. Now, if you divided your square in half
so as to produce Fig. 35 it is possible to cut it into as few as three
pieces to form a Greek cross. We thus save a piece.

I give another puzzle in Fig. 36. The dotted lines are added merely to
show the correct proportions of the figure--a square of 25 cells with
the four corner cells cut out. The puzzle is to cut this figure into
five pieces that will form a Greek cross (entire) and a square.

[Illustration: FIG. 35.]

[Illustration: FIG. 36.]

The solution to the first of the two puzzles last given--to cut a
rectangle of the shape of a half-square into three pieces that will form
a Greek cross--is shown in Figs. 37 and 38. It will be seen that we
divide the long sides of the oblong into six equal parts and the short
sides into three equal parts, in order to get the points that will
indicate the direction of the cuts. The reader should compare this
solution with some of the previous illustrations. He will see, for
example, that if we continue the cut that divides B and C in the cross,
we get Fig. 15.

[Illustration: FIG. 37.]

[Illustration: FIG. 38.]

The other puzzle, like the one illustrated in Figs. 12 and 13, will show
how useful a little arithmetic may sometimes prove to be in the solution
of dissection puzzles. There are twenty-one of those little square cells
into which our figure is subdivided, from which we have to form both a
square and a Greek cross. Now, as the cross is built up of five squares,
and 5 from 21 leaves 16--a square number--we ought easily to be led to
the solution shown in Fig. 39. It will be seen that the cross is cut out
entire, while the four remaining pieces form the square in Fig. 40.

[Illustration: FIG. 39]

[Illustration: FIG. 40]

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