If p is the perimeter of a right angle triangle with integral length sides, {a,b,c}, there are exactly three solutions for p = 120:
{20,48,52}, {24,45,51}, {30,40,50}
For which value of p ≤ 1000, is the number of solutions maximised?
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from math import ceil
from statistics import mode
# just guessing an upper bound of side length
s = 500
# create a list of pythagorean triplets
# i.e. sets of side length for right-angled triangles
pytrip = []
for a in range(1,s):
for b in range(1,s):
# pythagoras
c = ((a*a + b*b)**0.5)
# c is float: checking if it is an integer
if ceil(c) == c:
# create triplet in a list to be summed later
pytrip.append([a,b,int(c)])
# create a data set of perimeters of right angle triangles
data = []
for triple in pytrip:
data.append(sum(triple))
# perimeter that occurs most frequently for every triples
# with s < 499
print(mode(data))