ANSWER

8 - 11 year olds

It is only possible if the lenght of any stick is smaller than the length of the sum of the lengths of the other two.

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By proving that the largest has length IS SMALLER than the sum of the lengths of the other two, we know whether a triangle is formed or not.

9 is smaller than 5 + 8. So we can create a triangle with 5, 8 and 9.

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10 = 3 + 7. There is no possible triangle with 10, 3 and 7.

a-- 13 is smaller than 4 + 6. There is no possible triangle with 4, 6 and 13.

b--  Since the stick we are looking for must be less than 6, then 11 (one of the given sides) must be the greatest length. So, 11 must be less than the sum of 11 (the other given side) + the one we look for.

This will always happen. The solutions are 1, 2, 3, 4, and 5.

c-- A triangle will always be formed, as we have explained in the previous section. Therefore, there is no solution for section c.