Find the Number of non-congruent triangles (integer sided) whose sides belong to the set
This is a question in a national level based examination. Now in here what i can see that be taking each of the numbers as largest side(except for 10 and 11) we can find the number of triangles thus formed in each case by a brute force method.
Now also the question says non congruent triangles which makes the problem even more complex.Now do we apply recurssion here or simply this a problem of permutations and combinations.
Also i accept that my method of a brute force approach is rather an unintelligent way to solve it,so i am looking for answer that can solve it in 5 lines or so.