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What is the minimum number of squares a 13 by 13 square can be dissected into?

Paving the Way

Age 11 to 14 Challenge Level:

If the number of tiles used originally was x 2 and the total number of tiles used was y 2 , then :

x 2 + 100 = y 2
x 2 + 10 2 = y 2

This is a Pythagorean triple (see Pythagorean Triples ) which can be satisfied by x = 24 with y = 26.
So total number of tiles = 26 2 = 676

Correct solution from Adrian from South Greenhoe Middle School.