1. There are 9 sticks of different lengths from 1 cm to 9 cm. What are the side lengths of the squares that can be formed from these sticks, and in how many ways can they be formed? Ways of forming a square are considered different if different sticks are used and not necessarily all of them.

Can squares with side lengths of 1 cm, 2 cm, ... 6 cm be formed? Why? Can a square with a side length of 7 cm be formed? How can it be done? In how many different ways can it be formed? Consider all possible cases. Can a square with a side length of 12 cm or more be formed? Why?
1. Solution. One way to form squares is to have side lengths of $7 \mathrm{~cm}, 8 \mathrm{~cm}, 10 \mathrm{~cm}, 11 \mathrm{~cm}$. In five ways, squares can be formed, each with a side length of $9 \mathrm{~cm}$. Thus, there are 9 ways to form the squares.

Hint. The side length of the square must be greater than 6 cm (Why?). Since the total length of all the sticks is 45 cm, the perimeter of the square cannot be more than 44 cm, and the side length of the square cannot be more than $11 \mathrm{~cm}$. (MvSh)