How many squares does a (regular) chessboard have?

I know its 204 but I have no idea how to justify it.

Also, how many rectangles does a (regular) chessboard have?

TacoBell Sep 13, 2020

#1**+2 **

See this for squares: http://puzzles.nigelcoldwell.co.uk/twentyseven.htm

For rectangles:

We can choose the two verticals in \(\binom{8+1}{2}=36\) ways, and by symmetry, it is the same for horizontals. So 36^2=**1296.**

thedudemanguyperson Sep 13, 2020

#3**+2 **

No problem. The technique with choose binomials is very helpful in geometric counting/probability.

thedudemanguyperson
Sep 13, 2020