# Induction problem 3

### Hints on why the claim is true

It's obvious how to divide a square into 4 smaller squares. That
doesn't directly help you with this claim (which starts at n=6), but
perhaps the division into four might be useful in an indirect way.

Try dividing one of the squares into smaller squares. How does this
change the number of squares?

For n=6, we can cut up the
square as follows, where the side length of the big square is twice
that of the smaller squares.

6 Squares
________
|__|__|__|
| |__|
|_____|__|

Can you generalize the construction for n=6 to work for any other number of
subsquares?

Make a table of solutions you've found for different values of n.

It's convenient if all the solutions look very similar.
However, it's also ok if you need to use different methods for
different values of n, e.g. one method for the odd numbers and
one for the even numbers.