+210 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?
+600 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.
+600 No problem. The technique with choose binomials is very helpful in geometric counting/probability.
