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											2018-10-10 18:03:03 -04:00
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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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										 |  |  | forumTopicId: 302025 | 
					
						
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											2021-01-13 03:31:00 +01:00
										 |  |  | dashedName: problem-364-comfortable-distance | 
					
						
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											2018-10-10 18:03:03 -04:00
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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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							|  |  |  | 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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							|  |  |  | ```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 | 
					
						
							|  |  |  | function euler364() { | 
					
						
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							|  |  |  |   return true; | 
					
						
							|  |  |  | } | 
					
						
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							|  |  |  | euler364(); | 
					
						
							|  |  |  | ``` | 
					
						
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										 |  |  | # --solutions--
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										 |  |  | ```js | 
					
						
							|  |  |  | // solution required | 
					
						
							|  |  |  | ``` |