2018-09-30 23:01:58 +01:00
										 
									 
								 
							 | 
							
								
							 | 
							
								
							 | 
							
							
								---
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								id: 5900f44b1000cf542c50ff5d
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								challengeType: 5
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								title: 'Problem 222: Sphere Packing'
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								---
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								## Description
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								<section id='description'>
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								What is the length of the shortest pipe, of internal radius 50mm, that can fully contain 21 balls of radii 30mm, 31mm, ..., 50mm?
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								Give your answer in micrometres (10-6 m) rounded to the nearest integer.
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								</section>
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								## Instructions
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								<section id='instructions'>
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								</section>
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								## Tests
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								<section id='tests'>
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								```yml
							 | 
						
					
						
							
								
									
										
										
										
											2018-10-04 14:37:37 +01:00
										 
									 
								 
							 | 
							
								
									
										
									
								
							 | 
							
								
							 | 
							
							
								tests:
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								  - text: <code>euler222()</code> should return 1590933.
							 | 
						
					
						
							
								
									
										
										
										
											2018-10-20 21:02:47 +03:00
										 
									 
								 
							 | 
							
								
									
										
									
								
							 | 
							
								
							 | 
							
							
								    testString: assert.strictEqual(euler222(), 1590933, '<code>euler222()</code> should return 1590933.');
							 | 
						
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 
									 
								 
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								```
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								</section>
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								## Challenge Seed
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								<section id='challengeSeed'>
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								<div id='js-seed'>
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								```js
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								function euler222() {
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								  // Good luck!
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								  return true;
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								}
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								euler222();
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								```
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								</div>
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								</section>
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								## Solution
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								<section id='solution'>
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								```js
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								// solution required
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								```
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								</section>
							 |