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								---
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								id: 5900f4411000cf542c50ff54
							 
						 
					
						
							
								
									
										
										
										
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								title: 'Problem 213: Flea Circus'
							 
						 
					
						
							
								
									
										
										
										
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								challengeType: 5
							 
						 
					
						
							
								
									
										
										
										
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								forumTopicId: 301855
							 
						 
					
						
							
								
									
										
										
										
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								dashedName: problem-213-flea-circus
							 
						 
					
						
							
								
									
										
										
										
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								---
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
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								# --description--
  
						 
					
						
							
								
									
										
										
										
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								A 30× 
							 
						 
					
						
							
								
									
										
										
										
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								When a bell is rung, each flea jumps to an adjacent square at random (usually 4 possibilities, except for fleas on the edge of the grid or at the corners).
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								What is the expected number of unoccupied squares after 50 rings of the bell? Give your answer rounded to six decimal places.
							 
						 
					
						
							
								
									
										
										
										
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								# --hints--
  
						 
					
						
							
								
									
										
										
										
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								`euler213()`  should return 330.721154. 
						 
					
						
							
								
									
										
										
										
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								```js
							 
						 
					
						
							
								
									
										
										
										
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								assert.strictEqual(euler213(), 330.721154);
							 
						 
					
						
							
								
									
										
										
										
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								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
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								# --seed--
  
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								## --seed-contents--
  
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								function euler213() {
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								  return true;
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								}
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								euler213();
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
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								# --solutions--
  
						 
					
						
							
								
									
										
										
										
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								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								// solution required
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
								
									
								 
							
							
								```