square fitting

interestingly, there are other representations

the smallest square filled with 21 squares of different sizes, discovered by AJW Duijvestijn in 1978 according to David Wells (in 'Curious and Interesting Geometry') is shown below

• the littlest square is 2 by 2
• the next littlest is 4 by 4
• the next littlest is 6 by 6
• and the next littlest is 7 by 7

what must each other size of square be?

a related task is to fit together squares with Fibonnacci numbers as the dimensions of their sides:

see also some work on expressions