Question

The three sides of a triangle have length a, b and c. Each is an integer and a ≤ b ≤ c. If c = 7, how many such triangle are possible?

Answer 1

for example 1,2,7 is impossible because 1+2 will not reach 7
so the smallest sum of a and b must be bigger than 7
1 6 7 is still too small
so
2 6 7
3 5 7
3 6 7
4 4 7
4 5 7
4 6 7
5 6 7