2018-09-30 22:01:58 +00:00
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---
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id: 5900f4591000cf542c50ff6c
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title: 'Problem 237: Tours on a 4 x n playing board'
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2020-11-27 18:02:05 +00:00
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challengeType: 5
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2019-08-05 16:17:33 +00:00
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forumTopicId: 301882
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2021-01-13 02:31:00 +00:00
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dashedName: problem-237-tours-on-a-4-x-n-playing-board
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2018-09-30 22:01:58 +00:00
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---
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2020-11-27 18:02:05 +00:00
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# --description--
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2018-09-30 22:01:58 +00:00
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Let T(n) be the number of tours over a 4 × n playing board such that:
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2020-11-27 18:02:05 +00:00
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2018-09-30 22:01:58 +00:00
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The tour starts in the top left corner.
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2020-11-27 18:02:05 +00:00
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2018-09-30 22:01:58 +00:00
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The tour consists of moves that are up, down, left, or right one square.
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2020-11-27 18:02:05 +00:00
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The tour visits each square exactly once.
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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The tour ends in the bottom left corner.
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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The diagram shows one tour over a 4 × 10 board:
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2018-09-30 22:01:58 +00:00
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T(10) is 2329. What is T(1012) modulo 108?
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2020-11-27 18:02:05 +00:00
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# --hints--
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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`euler237()` should return 15836928.
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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```js
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assert.strictEqual(euler237(), 15836928);
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2018-09-30 22:01:58 +00:00
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```
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2020-11-27 18:02:05 +00:00
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# --seed--
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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## --seed-contents--
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2018-09-30 22:01:58 +00:00
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```js
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function euler237() {
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2020-09-15 16:57:40 +00:00
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2018-09-30 22:01:58 +00:00
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return true;
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}
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euler237();
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```
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2020-11-27 18:02:05 +00:00
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# --solutions--
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2018-09-30 22:01:58 +00:00
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```js
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// solution required
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```
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