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								---
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								id: 5900f4f61000cf542c510008
							 
						 
					
						
							
								
									
										
										
										
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								title: 'Problem 393: Migrating ants'
							 
						 
					
						
							
								
									
										
										
										
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								challengeType: 5
							 
						 
					
						
							
								
									
										
										
										
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								forumTopicId: 302058
							 
						 
					
						
							
								
									
										
										
										
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								dashedName: problem-393-migrating-ants
							 
						 
					
						
							
								
									
										
										
										
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								---
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
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								# --description--
  
						 
					
						
							
								
									
										
										
										
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								An n× 
							 
						 
					
						
							
								
									
										
										
										
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								All ants decide to move simultaneously to an adjacent square (usually 4 possibilities, except for ants on the edge of the grid or at the corners).
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								We define f(n) to be the number of ways this can happen without any ants ending on the same square and without any two ants crossing the same edge between two squares.
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								You are given that f(4) = 88. Find f(10).
							 
						 
					
						
							
								
									
										
										
										
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								# --hints--
  
						 
					
						
							
								
									
										
										
										
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								`euler393()`  should return 112398351350823100. 
						 
					
						
							
								
									
										
										
										
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								```js
							 
						 
					
						
							
								
									
										
										
										
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								assert.strictEqual(euler393(), 112398351350823100);
							 
						 
					
						
							
								
									
										
										
										
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								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
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								# --seed--
  
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								## --seed-contents--
  
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								function euler393() {
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								  return true;
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								}
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								euler393();
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
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								# --solutions--
  
						 
					
						
							
								
									
										
										
										
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								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								// solution required
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								```