3. Find all possible values of the perimeter of a rectangle, given that it can be cut into three rectangles, the perimeter of each of which is 10, and the side lengths are integers.
Answer: $14,16,18,22$ or 26.

Solution. There are two possible ways of cutting.

1) The cut lines are parallel. Let $x$ be the length of one side of one of the rectangles in the partition, then it is not difficult to express the other sides. In this case, $1 \leq x \leq 4$, so the perimeter of the original rectangle is $2(2 x+5)=14,18,22$ or 26.
2) The cut lines are perpendicular. Similarly, denoting by $x$ the length of one side of one of the rectangles, we find the lengths of the other sides. Then $1 \leq x \leq 2$, so the perimeter of the original rectangle is $2(10-x)=16$ or 18.

Comment. 4 points for each correct answer.