data/problems/90.yml
---
:id: 90
:name: Cube digit pairs
:url: https://projecteuler.net/problem=90
:content: "Each of the six faces on a cube has a different digit (0 to 9) written
on it; the same is done to a second cube. By placing the two cubes side-by-side
in different positions we can form a variety of 2-digit numbers.\n\nFor example,
the square number 64 could be formed:\n\n  \n\nIn
fact, by carefully choosing the digits on both cubes it is possible to display all
of the square numbers below one-hundred: 01, 04, 09, 16, 25, 36, 49, 64, and 81.\n\nFor
example, one way this can be achieved is by placing {0, 5, 6, 7, 8, 9} on one cube
and {1, 2, 3, 4, 8, 9} on the other cube.\n\nHowever, for this problem we shall
allow the 6 or 9 to be turned upside-down so that an arrangement like {0, 5, 6,
7, 8, 9} and {1, 2, 3, 4, 6, 7} allows for all nine square numbers to be displayed;
otherwise it would be impossible to obtain 09.\n\nIn determining a distinct arrangement
we are interested in the digits on each cube, not the order.\n\n{1, 2, 3, 4, 5,
6} is equivalent to {3, 6, 4, 1, 2, 5} \n{1, 2, 3, 4, 5, 6} is distinct from {1,
2, 3, 4, 5, 9}\n\nBut because we are allowing 6 and 9 to be reversed, the two distinct
sets in the last example both represent the extended set {1, 2, 3, 4, 5, 6, 9} for
the purpose of forming 2-digit numbers.\n\nHow many distinct arrangements of the
two cubes allow for all of the square numbers to be displayed?\n\n"