How many non-congruent triangles are there with sides of integer length having at least one side of length six units and having no side longer than six units?
One side of the triangle must be 6.
Then, if the second side is also 6, the third side can be either 6, 5, 4, 3, 2, or 1 -- 6 possibilities.
If the second side is 5, the third side can be either 5, 4, 3, or 2 -- 4 possibilities.
If the second side is 4, the third side can be either 4 or 3 -- 2 possibilities.
The second side cannot be shorted than 4.
Did I miss any?