Question: how many different triangles can be made with a perimeter of 12 matches?
Answer: There are three distinct triangles using 12 matchsticks: 3-4-5,4-4-4, and 5-5-2. Note that for a given number of matchsticks M, if the sides of the triangle are labeled a,b, and c (without loss of generality let c be the longest side) then a+b+c=M, a+b>c and c<M/2.