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								id: 5900f4d91000cf542c50ffea
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								title: 'Problem 364: Comfortable distance'
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								challengeType: 5
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											2019-08-05 09:17:33 -07:00
										 
									 
								 
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								forumTopicId: 302025
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											2021-01-13 03:31:00 +01:00
										 
									 
								 
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								dashedName: problem-364-comfortable-distance
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								---
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											2020-11-27 19:02:05 +01:00
										 
									 
								 
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								# --description--
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								There are N seats in a row. N people come after each other to fill the seats according to the following rules:
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								If there is any seat whose adjacent seat(s) are not occupied take such a seat.
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								If there is no such seat and there is any seat for which only one adjacent seat is occupied take such a seat.
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											2018-10-08 01:01:53 +01:00
										 
									 
								 
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								Otherwise take one of the remaining available seats.
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								Let T(N) be the number of possibilities that N seats are occupied by N people with the given rules. The following figure shows T(4)=8.
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								We can verify that T(10) = 61632 and T(1 000) mod 100 000 007 = 47255094. Find T(1 000 000) mod 100 000 007.
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								# --hints--
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								`euler364()` should return 44855254.
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											2020-11-27 19:02:05 +01:00
										 
									 
								 
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								```js
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								assert.strictEqual(euler364(), 44855254);
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								```
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								# --seed--
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								## --seed-contents--
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								```js
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								function euler364() {
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											2020-09-15 09:57:40 -07:00
										 
									 
								 
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								  return true;
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								}
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								euler364();
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								```
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								# --solutions--
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								```js
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								// solution required
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								```
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