Hi.Can someone please clarify. The formula for number of scalene triangles with given even parameter is (p-6)^2/48 but it does not hold for p=6. Is this an exception only ? as 1,2,3 is a scalene triangle possible.

My bad. 1,2,3 is not a triangle. And for other numbers, we have to take nearest integer not greatest integer.

For 7, and 8, it'll be 0. You can even verify it manually, and through the formula.

For p=9, you'll get 0.75 through the formula. Rounded off to 1.

Even if you try manually, you'll get 2,3,4 as the only scalene triangle.

1,2,3 cannot be a scalene triangle as it doesn't satisfy the triangle inequality theorem. For the cases of perimeter as 7 and 9 the formulae changes
when p is odd (p-3)^2/48

You have to add 1 in the solution when p is even multiple of 3.
But still you should cross check with some teacher.

Even for perimeter=7,8,9. I am not getting the right answer. Can someone please clarify.