[ [equations in integers $]$ ]

In the room, there are three-legged stools and four-legged chairs. When people sat on all these seats, there were 39 legs in the room.

How many stools are in the room?
According to the condition, there are five- and six-legged creatures in the room, with a total of 39 legs. The number of legs of the five-legged creatures ends in 0 or 5. But it cannot end in 0: then the number of legs of the six-legged creatures would end in 9. In such a case, the number of five-legged creatures can be 1, 3, 5, or 7. By trial and error, we determine that there are 3 five-legged creatures and 4 six-legged creatures. That is, there are 4 chairs and 3 stools in the room.

## Answer

3 stools.