Hello, baxteryay!

This is based on a classic problem.

Answer: his chain had from 8 to 15 links.

Suppose his chain had 7 links.

He could cut one link like this: .

Then he can present from 1 to 7 links.

. .

Since he neededcuts, he had more than 7 links,two

. . up to a maximum of 15 links.

Suppose his chain had 15 links.

Again, he would cut the 3rd link . . . and cut the 7th link.

This gives him four chains with 2, 1, 4, and 8 links.

Then he can present from 1 to 15 links.