Sal cuts a square of integer side length into smaller squares of integer side length. For example, she might cut a $4*4$ square into four $1*1$ squares and three $2*2$ squares, making 7 pieces.
A. Draw a diagram to show how Sal can cut a $5*5$ square into 11 square pieces.
I've completed this one. I was just wondering is there a formula or proof to show the relation?
B. Show that Sal can't cut a $4*4$ square into 11 pieces
I've done this by showing all of the possible cuts for a $4*4$ square, however that's not very convenient. Is there some sort of formula/shortcut/proof for it?
C. Sal has 2 $4*4$ squares, 3 $3*3$ squares, 4 $2*2$ squares and 4 $1*1$ squares. Draw a diagram showing how she can place all or some of these squares together without gaps or overlaps to make the largest square possible. Explain why she cannot construct a larger square.
Here is where I'm having problems. This question almost certainly requires the use of proofs, and I'm not very good at those. So is there some proof I can use to make the biggest square possible and why isn't there a bigger square.