A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
a2 + b2 = c2
For example, 32 + 42 = 9 + 16 = 25 = 52.
There exists exactly one Pythagorean triplet for which
a + b + c= 1000.
Find the product
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
b can get bigger than
500. This means that we can set our upper limit to
a < b it makes sense to start searching for
a + 1. For each such pair of
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
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