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								---
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								id: 5900f5101000cf542c510022
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								title: 'Problem 419: Look and say sequence'
							 
						 
					
						
							
								
									
										
										
										
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								challengeType: 5
							 
						 
					
						
							
								
									
										
										
										
											2019-08-05 09:17:33 -07:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								forumTopicId: 302088
							 
						 
					
						
							
								
									
										
										
										
											2021-01-13 03:31:00 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								dashedName: problem-419-look-and-say-sequence
							 
						 
					
						
							
								
									
										
										
										
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								---
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
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								# --description--
  
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
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								The look and say sequence goes 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, ...
							 
						 
					
						
							
								
									
										
										
										
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								The sequence starts with 1 and all other members are obtained by describing the previous member in terms of consecutive digits.
							 
						 
					
						
							
								
									
										
										
										
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								It helps to do this out loud:
							 
						 
					
						
							
								
									
										
										
										
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								1 is 'one one' → 11
							 
						 
					
						
							
								
									
										
										
										
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								11 is 'two ones' → 21
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
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								21 is 'one two and one one' → 1211
							 
						 
					
						
							
								
									
										
										
										
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								1211 is 'one one, one two and two ones' → 111221
							 
						 
					
						
							
								
									
										
										
										
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								111221 is 'three ones, two twos and one one' → 312211
							 
						 
					
						
							
								
									
										
										
										
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								...
							 
						 
					
						
							
								
									
										
										
										
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								Define A(n), B(n) and C(n) as the number of ones, twos and threes in the n'th element of the sequence respectively. One can verify that A(40) = 31254, B(40) = 20259 and C(40) = 11625.
							 
						 
					
						
							
								
									
										
										
										
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								Find A(n), B(n) and C(n) for n = 1012. Give your answer modulo 230 and separate your values for A, B and C by a comma. E.g. for n = 40 the answer would be 31254,20259,11625
							 
						 
					
						
							
								
									
										
										
										
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								# --hints--
  
						 
					
						
							
								
									
										
										
										
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								`euler419()`  should return 998567458, 1046245404, 43363922. 
						 
					
						
							
								
									
										
										
										
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								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								assert.strictEqual(euler419(), 998567458, 1046245404, 43363922);
							 
						 
					
						
							
								
									
										
										
										
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								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
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								# --seed--
  
						 
					
						
							
								
									
										
										
										
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								## --seed-contents--
  
						 
					
						
							
								
									
										
										
										
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								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								function euler419() {
							 
						 
					
						
							
								
									
										
										
										
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								  return true;
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								}
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								euler419();
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
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								# --solutions--
  
						 
					
						
							
								
									
										
										
										
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								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								// solution required
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								```