Big Grid

Probability Level 2

Shown is a $3\times3$ grid containing $14$ squares. How many squares would there be in $100\times100$ grid?

The answer is 338350.

1 solution

Marta Reece
May 14, 2018

$1^1+2^2+...+n^2=\frac{n^3}3+\frac{n^2}2+\frac n6$

$1^1+2^2+...+100^2=\frac{1000000}3+\frac{10000}2+\frac {100}6=\boxed{338,350}$