536 Puzzles and Curious Problems

Answers 321

work just because its area is a square with side IS. Figure IV shows the

best that can be done in that case, but there are three pieces instead of

two as required. This is because 9 is not a multiple of the added height, 6, nor

25 a multiple of the reduced length, 10. Consequently, the steps cannot

be formed.

II

25

-------------l

--i!--: B i I DZ'

I I

9

(^5) B
z.s
Of course, any multiple of the sides will work. Thus, a board 8 X 18
is solved exactly like 4 X 9, in two steps, by just doubling all the measure-
ments. Similarly, a board 4 X 6\4 will work, for it is the same ratio as 16 X 25,
the steps being I in height and I \4 in breadth. In the former case we should
reduce it like a fraction, and in the second case multiply it by 4 to get rid of
the fraction. Then we should see that 4 X 9 and 16 X 25 were, in each case,
squares of consecutive numbers and know that a solution is possible.