Question 21
Jack has a long wooden stick of 30cm. He wants to divide it into 3 shorter sticks of integral lengths so that they can make up a triangle. For example, dividing into 3 sticks with side length 9cm, 10cm, 11cm is one way to do that. At most how many different triangles can Jack make?
Editorial convention: two triangles with the same three side lengths count as one, regardless of order; degenerate straight triangles are excluded.
Editorial convention: two triangles with the same three side lengths count as one, regardless of order; degenerate straight triangles are excluded.