project-euler/solutions/python/044.py at master · ThomasJackDalby/project-euler · GitHub

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"""
    Problem 44
    ==========


    Pentagonal numbers are generated by the formula, P[n]=n(3n−1)/2. The first
    ten pentagonal numbers are:

    1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...

    It can be seen that P[4] + P[7] = 22 + 70 = 92 = P[8]. However, their
    difference, 70 − 22 = 48, is not pentagonal.

    Find the pair of pentagonal numbers, P[j] and P[k], for which their sum
    and difference are pentagonal and D = |P[k] − P[j]| is minimised; what is
    the value of D?


    Answer: 2c2556cb85621309ca647465ffa62370
"""
from common import check
from itertools import count, takewhile

PROBLEM_NUMBER = 44
ANSWER_HASH = "2c2556cb85621309ca647465ffa62370"

pentagonals = set()

def get_pentagonal(n):
    t = int(n * (3 * n - 1) * 0.5)
    return t

D = None
for d in count(1):
    p_d = get_pentagonal(d)
    pentagonals.add(p_d)
    for c in range(d - 1, 0, -1):
        p_c = get_pentagonal(c)
        p_b = p_d - p_c
        p_a = p_c - p_b
        if p_b not in pentagonals or p_a not in pentagonals:
            continue

        check(p_a, PROBLEM_NUMBER, ANSWER_HASH)
        exit()