2018-09-30 23:01:58 +01:00
										 
									 
								 
							 | 
							
								
							 | 
							
								
							 | 
							
							
								---
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								id: 5900f42b1000cf542c50ff3d
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								challengeType: 5
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								title: 'Problem 190: Maximising a weighted product'
							 | 
						
					
						
							
								
									
										
										
										
											2019-08-05 09:17:33 -07:00
										 
									 
								 
							 | 
							
								
									
										
									
								
							 | 
							
								
							 | 
							
							
								forumTopicId: 301828
							 | 
						
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 
									 
								 
							 | 
							
								
							 | 
							
								
							 | 
							
							
								---
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								## Description
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								<section id='description'>
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								Let Sm = (x1, x2, ... , xm) be the m-tuple of positive real numbers with x1 + x2 + ... + xm = m for which Pm = x1 * x22 * ... * xmm is maximised.
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								For example, it can be verified that [P10] = 4112 ([ ] is the integer part function).
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								Find Σ[Pm] for 2 ≤ m ≤ 15.
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								</section>
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								## Instructions
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								<section id='instructions'>
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								</section>
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								## Tests
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								<section id='tests'>
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								```yml
							 | 
						
					
						
							
								
									
										
										
										
											2018-10-04 14:37:37 +01:00
										 
									 
								 
							 | 
							
								
									
										
									
								
							 | 
							
								
							 | 
							
							
								tests:
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								  - text: <code>euler190()</code> should return 371048281.
							 | 
						
					
						
							
								
									
										
										
										
											2019-07-26 19:26:37 -07:00
										 
									 
								 
							 | 
							
								
									
										
									
								
							 | 
							
								
							 | 
							
							
								    testString: assert.strictEqual(euler190(), 371048281);
							 | 
						
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 
									 
								 
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								```
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								</section>
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								## Challenge Seed
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								<section id='challengeSeed'>
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								<div id='js-seed'>
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								```js
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								function euler190() {
							 | 
						
					
						
							
								
									
										
										
										
											2020-09-15 09:57:40 -07:00
										 
									 
								 
							 | 
							
								
									
										
									
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 
									 
								 
							 | 
							
								
							 | 
							
								
							 | 
							
							
								  return true;
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								}
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								euler190();
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								```
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								</div>
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								</section>
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								## Solution
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								<section id='solution'>
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								```js
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								// solution required
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								```
							 | 
						
					
						
							
								
									
										
										
										
											2019-07-18 08:24:12 -07:00
										 
									 
								 
							 | 
							
								
									
										
									
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 
									 
								 
							 | 
							
								
							 | 
							
								
							 | 
							
							
								</section>
							 |