1.5 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f3ea1000cf542c50fefd | Problem 126: Cuboid layers | 5 | 301753 | problem-126-cuboid-layers |
--description--
The minimum number of cubes to cover every visible face on a cuboid measuring 3 x 2 x 1 is twenty-two.
If we 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.
However, 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.
We 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
.
It turns out that 154 is the least value of n
for which C(n) = 10
.
Find the least value of n
for which C(n) = 1000
.
--hints--
cuboidLayers()
should return 18522
.
assert.strictEqual(cuboidLayers(), 18522);
--seed--
--seed-contents--
function cuboidLayers() {
return true;
}
cuboidLayers();
--solutions--
// solution required