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.