Given 12 sticks of the same length. How can you cut them into smaller sticks so that you can form 13 equal triangles, with each of the smaller sticks being a side of one of these triangles?

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We need to form triangles with sides in the ratio of $3: 4: 5$.

## Solution

Let's assume the length of each stick is 13. We will cut three sticks into segments of length $3,3,3,4$; four sticks into segments of length 3, 5, 5; and five sticks into segments of length 4, 4, 5. As a result, we will have 13 sticks of length 3, 13 sticks of length 4, and 13 sticks of length 5. From these, we can form 13 equal triangles with sides $3,4,5$.

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