120 Geometrical Problemsa square has been formed with ten
square tiles. As ten is not a square
number a certain number of tiles must
be cut. In this case it is six. It will be
seen that the pieces I and I are cut
from one tile, 2 and 2 from another,
and so on.
If you had to cover a square space
with exactly twenty-nine square tiles
of equal size, how would you do it?
cut in two parts. A familiar exam- What is the smallest number of tiles
pie is shown in our illustration, where that you need cut in two parts?- SQUARE OF SQUARES
Cutting only along the lines, what is the smallest number of square pieces
into which the diagram can be dissected? The largest number possible is, of
course, 169, where all the pieces will be of the same size-one cell-but
we want the smallest number. We might cut away the border on two sides,
leaving one square 12 X 12, and cutting the remainder in 25 little squares,
making 26 in all. This is better than 169, but considerably more than the
fewest possible.