Take a 7x7 grid of squares and remove the center square.
Take two 5x5 grids of squares and remove each center square.
Cut the smaller figures into as few pieces as possible and reassemble to form the larger.
Is it possible to use fewer pieces if you are allowed to remove a different square than the center any of the original shapes?
Cut both smaller squares the same way into two pieces each:
XXXXX
XXXXX
YY XX
YYYYY
YYYYY
These can be arranged to form the larger figure:
AAAAABB
AAAAABB
DDDAABB
DDD BBB
DDCCBBB
DDCCCCC
DDCCCCC
This is the minimum number of pieces. The four corners of the large square must be from separate pieces, thus the minimum is four pieces.
Solution
