2018-09-30 22:01:58 +00:00
---
id: 5900f4b11000cf542c50ffc3
title: 'Problem 324: Building a tower'
2020-11-27 18:02:05 +00:00
challengeType: 5
2019-08-05 16:17:33 +00:00
forumTopicId: 301981
2021-01-13 02:31:00 +00:00
dashedName: problem-324-building-a-tower
2018-09-30 22:01:58 +00:00
---
2020-11-27 18:02:05 +00:00
# --description--
2018-09-30 22:01:58 +00:00
Let f(n) represent the number of ways one can fill a 3× 3× n tower with blocks of 2× 1× 1. You're allowed to rotate the blocks in any way you like; however, rotations, reflections etc of the tower itself are counted as distinct.
2020-11-27 18:02:05 +00:00
2018-09-30 22:01:58 +00:00
For example (with q = 100000007) :f(2) = 229,f(4) = 117805,f(10) mod q = 96149360,f(103) mod q = 24806056,f(106) mod q = 30808124.
Find f(1010000) mod 100000007.
2020-11-27 18:02:05 +00:00
# --hints--
2018-09-30 22:01:58 +00:00
2020-11-27 18:02:05 +00:00
`euler324()` should return 96972774.
2018-09-30 22:01:58 +00:00
2020-11-27 18:02:05 +00:00
```js
assert.strictEqual(euler324(), 96972774);
2018-09-30 22:01:58 +00:00
```
2020-11-27 18:02:05 +00:00
# --seed--
2018-09-30 22:01:58 +00:00
2020-11-27 18:02:05 +00:00
## --seed-contents--
2018-09-30 22:01:58 +00:00
```js
function euler324() {
2020-09-15 16:57:40 +00:00
2018-09-30 22:01:58 +00:00
return true;
}
euler324();
```
2020-11-27 18:02:05 +00:00
# --solutions--
2018-09-30 22:01:58 +00:00
```js
// solution required
```