project_euler.problem_062.sol1

Project Euler 62 https://projecteuler.net/problem=62

The cube, 41063625 (345^3), can be permuted to produce two other cubes: 56623104 (384^3) and 66430125 (405^3). In fact, 41063625 is the smallest cube which has exactly three permutations of its digits which are also cube.

Find the smallest cube for which exactly five permutations of its digits are cube.

Functions

get_digits(→ str)	Computes the sorted sequence of digits of the cube of num.
solution(→ int)	Iterate through every possible cube and sort the cube's digits in

Module Contents

project_euler.problem_062.sol1.get_digits(num: int) → str

Computes the sorted sequence of digits of the cube of num.

>>> get_digits(3)
'27'
>>> get_digits(99)
'027999'
>>> get_digits(123)
'0166788'

project_euler.problem_062.sol1.solution(max_base: int = 5) → int

Iterate through every possible cube and sort the cube’s digits in ascending order. Sorting maintains an ordering of the digits that allows you to compare permutations. Store each sorted sequence of digits in a dictionary, whose key is the sequence of digits and value is a list of numbers that are the base of the cube.

Once you find 5 numbers that produce the same sequence of digits, return the smallest one, which is at index 0 since we insert each base number in ascending order.

>>> solution(2)
125
>>> solution(3)
41063625