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Read carefully the problem and what should be the output, you are getting it:
"Because according to your answer that is 6 which is only possible when you add all the right triangles of length <50"
Well,the question is clear, but the example about "120" is absurd.By following the question 120 has 22 possibilities of forming a integer sided triangle.
I can see in your profile that you are Indian, and I suppose that English is not your native language. Many times the problem statement is an extra challenge for us that do not speak English natively, and is something that we must learn to overcome. A single word can change the things a lot, and the answer of the problem.
Yup...I completely agree with you on that...and btw it's "for us who do not" not "for us 'that' do not"...:P..no offence...:)