A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,

a

^{2}+ b^{2}= c^{2}For example, 3

^{2}+ 4^{2}= 9 + 16 = 25 = 5^{2}.There exists exactly one Pythagorean triplet for which

`a + b + c`

= 1000.

Find the product`abc`

.

So, here we are, we have the sum and we know that `a < b < c`

and on paper the sides would make a right-angled triangle. That gives us `a + b > c`

as we can't have a triangle where the sum of the lenghts of two of its sides would be smaller than the length of the third one. For this case it means that `c`

can't be bigger than `500`

, and as it is as well the biggest of the three numbers it also implies that neither `a`

nor `b`

can get bigger than `500`

. This means that we can set our upper limit to `nr/2`

. As `a < b`

it makes sense to start searching for `b`

at `a + 1`

. For each such pair of `a`

and `b`

we get `c`

by substracting them from the target sum and if it works in the Pythagorean equation, we return it.

`fn getTripleForSum nr =`

`(`

`local half = nr/2`

`local a, b, c`

`for a = 1 to half do`

`for b = (a + 1) to half do`

`(`

`c = nr - a - b`

`if c^2 == (a^2 + b^2) do`

`return a*b*c`

`)`

`)`

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