1.6 KiB
1.6 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f41a1000cf542c50ff2d | Problem 174: Counting the number of "hollow" square laminae that can form one, two, three, ... distinct arrangements | 5 | 301809 | problem-174-counting-the-number-of-hollow-square-laminae-that-can-form-one-two-three-----distinct-arrangements |
--description--
We shall define a square lamina to be a square outline with a square "hole" so that the shape possesses vertical and horizontal symmetry.
Given eight tiles it is possible to form a lamina in only one way: 3x3 square with a 1x1 hole in the middle. However, using thirty-two tiles it is possible to form two distinct laminae.
If t
represents the number of tiles used, we shall say that t = 8
is type L(1)
and t = 32
is type L(2)
.
Let N(n)
be the number of t ≤ 1000000
such that t
is type L(n)
; for example, N(15) = 832
.
What is \sum N(n)
for 1 ≤ n ≤ 10
?
--hints--
hollowSquareLaminaeDistinctArrangements()
should return 209566
.
assert.strictEqual(hollowSquareLaminaeDistinctArrangements(), 209566);
--seed--
--seed-contents--
function hollowSquareLaminaeDistinctArrangements() {
return true;
}
hollowSquareLaminaeDistinctArrangements();
--solutions--
// solution required