data/problems/126.yml
---
:id: 126
:name: Cuboid layers
:url: https://projecteuler.net/problem=126
:content: "The minimum number of cubes to cover every visible face on a cuboid measuring
3 x 2 x 1 is twenty-two.\n\n 
\ \n\nIf we then add a second layer to this solid it would require forty-six cubes
to cover every visible face, the third layer would require seventy-eight cubes,
and the fourth layer would require one-hundred and eighteen cubes to cover every
visible face.\n\nHowever, the first layer on a cuboid measuring 5 x 1 x 1
also requires twenty-two cubes; similarly the first layer on cuboids measuring 5 x 3 x 1,
7 x 2 x 1, and 11 x 1 x 1 all contain forty-six
cubes.\n\nWe shall define C(_n_) to represent the number of cuboids that contain
_n_ cubes in one of its layers. So C(22) = 2, C(46) = 4, C(78) = 5, and C(118) =
8.\n\nIt turns out that 154 is the least value of _n_ for which C(_n_) = 10.\n\nFind
the least value of _n_ for which C(_n_) = 1000.\n\n"