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								---
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								id: 5900f4531000cf542c50ff65
							 
						 
					
						
							
								
									
										
										
										
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								title: 'Problem 230: Fibonacci Words'
							 
						 
					
						
							
								
									
										
										
										
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								challengeType: 5
							 
						 
					
						
							
								
									
										
										
										
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								forumTopicId: 301874
							 
						 
					
						
							
								
									
										
										
										
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								dashedName: problem-230-fibonacci-words
							 
						 
					
						
							
								
									
										
										
										
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								---
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
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								# --description--
  
						 
					
						
							
								
									
										
										
										
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								For any two strings of digits, A and B, we define FA,B to be the sequence (A,B,AB,BAB,ABBAB,...) in which each term is the concatenation of the previous two.
							 
						 
					
						
							
								
									
										
										
										
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								Further, we define DA,B(n) to be the nth digit in the first term of FA,B that contains at least n digits.
							 
						 
					
						
							
								
									
										
										
										
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								Example:
							 
						 
					
						
							
								
									
										
										
										
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								Let A=1415926535, B=8979323846. We wish to find DA,B(35), say.
							 
						 
					
						
							
								
									
										
										
										
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								The first few terms of FA,B are: 1415926535 8979323846 14159265358979323846 897932384614159265358979323846 14159265358979323846897932384614159265358979323846
							 
						 
					
						
							
								
									
										
										
										
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								Then DA,B(35) is the 35th digit in the fifth term, which is 9.
							 
						 
					
						
							
								
									
										
										
										
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								Now we use for A the first 100 digits of π behind the decimal point: 14159265358979323846264338327950288419716939937510 58209749445923078164062862089986280348253421170679
							 
						 
					
						
							
								
									
										
										
										
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								and for B the next hundred digits:
							 
						 
					
						
							
								
									
										
										
										
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								82148086513282306647093844609550582231725359408128 48111745028410270193852110555964462294895493038196 .
							 
						 
					
						
							
								
									
										
										
										
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								Find ∑n = 0,1,...,17 10n× × 
							 
						 
					
						
							
								
									
										
										
										
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								# --hints--
  
						 
					
						
							
								
									
										
										
										
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								`euler230()`  should return 850481152593119200. 
						 
					
						
							
								
									
										
										
										
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								```js
							 
						 
					
						
							
								
									
										
										
										
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								assert.strictEqual(euler230(), 850481152593119200);
							 
						 
					
						
							
								
									
										
										
										
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								```
							 
						 
					
						
							
								
									
										
										
										
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								# --seed--
  
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								## --seed-contents--
  
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								function euler230() {
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								  return true;
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								}
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								euler230();
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
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								# --solutions--
  
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
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								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								// solution required
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								```