1.4 KiB
1.4 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f5021000cf542c510014 | Problem 405: A rectangular tiling | 5 | 302073 | problem-405-a-rectangular-tiling |
--description--
We wish to tile a rectangle whose length is twice its width.
Let T(0)
be the tiling consisting of a single rectangle.
For n > 0
, let T(n)
be obtained from T( n- 1)
by replacing all tiles in the following manner:
The following animation demonstrates the tilings T(n)
for n
from 0 to 5:
Let f(n)
be the number of points where four tiles meet in T(n)
. For example, f(1) = 0
, f(4) = 82
and f({10}^9)\bmod {17}^7 = 126\\,897\\,180
.
Find f({10}^k)
for k = {10}^{18}
, give your answer modulo {17}^7
.
--hints--
rectangularTiling()
should return 237696125
.
assert.strictEqual(rectangularTiling(), 237696125);
--seed--
--seed-contents--
function rectangularTiling() {
return true;
}
rectangularTiling();
--solutions--
// solution required