11527 - Morning Walk

All about problems in Volume 115. If there is a thread about your problem, please use it. If not, create one with its number in the subject.

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11527 - Morning Walk

Post by Vytenis »

It seems that I do not fully understand the problem and given test cases. Could someone help me?
The way I understand the problem is the following. In the first morning in all 3 cases (from M to N, N to P and P to M) Peter walks by two segments that are at a right angle, i.e. through the legs of some right triangles. In the second morning, however, he walks straight between every pair of points, i.e. through the hypotenuse of the same 3 right triangles. As the number of steps is an integer, all right triangles should by Pythagorean. Thus we need to find all possible triples of Pythagorean triangles with hypotenuses summing to a given number S. However, in the first sample test case the provided answer is "3 4 5", and as there are no Pythagorean triangles with hypotenuse 3 or 4, my assumptions stated above must be wrong.

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