320 Answers- THE PIKA TES' FLAG
The illustration will show that the
flag need only be cut in two pieces-
along the zigzag line. If the lower piece
is then moved up one step we shall
get a flag with the required ten stripes.- THE CARPENTER'S PUZZLE
In order that it may be cut in two pieces, on the step principle, to form
a square, take any rectangular board whose sides are the squares of two con-
secutive whole numbers. Thus, in the following table, the square of 1 (1) and
the square of 2 (4); or 2 (4) and 3 (9); or 3 (9) and 4 (l6);-and so
on. The table may be extended to any length desired.
Sides No. of Steps Side of Square
1 X 4^1 2
4X9 2 6
9 X 16 3 12
16 X 25 4 20
25 X 36 5 30In Figure I is shown the simple case of a board 1 X 4, in Figure II the case
of 4 X 9, and Figure III shows the case of 16 X 25. It will be seen that
the number of steps increases regularly as we advance, but with the table they
are easily found. Thus, for the case 16 X 25, as the side of the square will be
20, the steps will be 20 - 16 = 4 in height and 25 - 20 = 5 in breadth.
As the sides are square numbers, and two square numbers multiplied
together always make another square, the area will always be a perfect
square. But we must not conclude from this that a board, say, 9 X 25 would