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Ah I had bad math. There is no way to take the derivative and get a simple formula. I got accepted by iterating thorugh angles and checking them.

I used trigonometry and derivative to calculate the maximum excursion of the piano into the corridor and if this value is less than the width it prints "Y", otherwise "N". In the test cases of course it works, and in drawings I have made it seems to work also. I have tried moving to next test case ...

Just take (x+1)^3 and expand symbolically. You get:

(x+1)^3 = x^3 + 3x^2 + 3x + 1

This assumes that the sum and the largest a[n]^3 are 1 apart, so the remaining terms fall within the rest of the formula. This may not be a good assumption, but since there are many solutions to each case (infinitely ...

I like this problem, it looks like there are many ways to solve it.

Maarten:

Your numbers are very large, how did you generate them? It is interesting that you get numbers of that size.

one&only:

Why are you randomly picking odd or even numbers? I did not use randomness and just did permutations ...