Question 333267
How many squares of all sizes can you find on a 6 by 6 checkerboard? their are 36 smaller squares in this 6 by 6 checkerboard.
<pre><b>
{{{drawing(300,300,-1,7,-1,7, 

line(0,0,6,0), line(1,0,1,6),line(2,0,2,6),line(3,0,3,6),line(4,0,4,6),line(5,0,5,6),line(6,0,6,6),

line(0,0,0,6),line(0,1,6,1),line(0,2,6,2),line(0,3,6,3),line(0,4,6,4),line(0,5,6,5),line(0,6,6,6) )}}}

There are 36 1x1 squares.
There are 25 2x2 squares.
There are 16 3x3 squares.
There are  9 4x4 squares.
There are  4 5x5 squares.
There is   1 6x6 squares. 

That's a total of 36+25+16+9+4+1=91 squares.

It's interesting that those numbers are the perfect squares

{{{1^2}}}, {{{2^2}}}, {{{3^2}}}, {{{4^2}}}, {{{5^2}}}, {{{6^2}}}

Edwin</pre>