# Square determination

A checkered flag used for racing is a square flag containing 64 alternating white and black squares. How many squares on the checkered flag contain an equal number of white and black squares? Be sure to describe how you arrived at your answer.

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#### Solution Preview

OK, here's the flag: http://en.wikipedia.org/wiki/File:Auto_Racing_Chequered.svg Unfortunately, this one is only 6 by 8, but we can pretend that we have a flag which is an 8 by 8 square.

If a square in this flag contains an equal number of white and black squares, its side must be an even number (otherwise, it contains an odd number of squares). So, we should count all squares of sizes 2x2, 4x4, 6x6 and 8x8.

There's only ...

#### Solution Summary

Square determination is established. 64 alternative which and black squares are examined.