First slide

Combinations

Question

The number of squares that we can find on a chess board is

Moderate

A

64
B

160
C

224
D

204

Solution

To get a square of size $r x r,$ we must choose $(r + 1)$ consecutive horizontal and $(r + 1)$ consecutive vertical lines. This can be done in $(9 - r) (9 - r) = {(9 - r)}^{2}$ ways.

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