Counting squares

Algebra Level 3

How many squares are in a 10 × 10 10\times10 grid?

Clarification: The squares can be of any size, e.g. 2 × 2 2\times2 , 3 × 3 3\times3 , etc.

Image credit: www.eduplace.com


The answer is 385.

View wiki
David Pilling by David Pilling , 18, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

David Pilling
May 13, 2016

There is 1 1 way to form a 10 x 10 10x10 grid, 4 4 ways to form a 9 x 9 9x9 grid, 9 9 ways to form an 8 x 8 8x8 grid etc. Each time there are n 2 n^2 ways where n = 11 − G n = 11-G for a G x G GxG grid. So, the total number of ways is 1 2 + 2 2 + 3 2 + . . . + 1 0 2 = 385 1^2 + 2^2 + 3^2 + ... + 10^2 = \boxed{385}

3 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...