2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								---
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								id: 5900f4e41000cf542c50fff5
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								title: 'Problem 375: Minimum of subsequences'
							 
						 
					
						
							
								
									
										
										
										
											2020-11-27 19:02:05 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								challengeType: 5
							 
						 
					
						
							
								
									
										
										
										
											2019-08-05 09:17:33 -07:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								forumTopicId: 302037
							 
						 
					
						
							
								
									
										
										
										
											2021-01-13 03:31:00 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								dashedName: problem-375-minimum-of-subsequences
							 
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								---
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2020-11-27 19:02:05 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								# --description--
  
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								Let Sn be an integer sequence produced with the following pseudo-random number generator:
							 
						 
					
						
							
								
									
										
										
										
											2020-11-27 19:02:05 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								S0
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2020-11-27 19:02:05 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								=
							 
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2020-11-27 19:02:05 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								290797
							 
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2020-11-27 19:02:05 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								Sn+1
							 
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2020-11-27 19:02:05 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								=
							 
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2020-11-27 19:02:05 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								Sn2 mod 50515093
							 
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2020-11-27 19:02:05 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								Let A(i, j) be the minimum of the numbers Si, Si+1, ... , Sj for i ≤ j. Let M(N) = ΣA(i, j) for 1 ≤ i ≤ j ≤ N. We can verify that M(10) = 432256955 and M(10 000) = 3264567774119.
							 
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2020-11-27 19:02:05 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								Find M(2 000 000 000).
							 
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2020-11-27 19:02:05 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								# --hints--
  
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2020-11-27 19:02:05 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								`euler375()`  should return 7435327983715286000. 
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2020-11-27 19:02:05 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								assert.strictEqual(euler375(), 7435327983715286000);
							 
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2020-11-27 19:02:05 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								# --seed--
  
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2020-11-27 19:02:05 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								## --seed-contents--
  
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								function euler375() {
							 
						 
					
						
							
								
									
										
										
										
											2020-09-15 09:57:40 -07:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								  return true;
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								}
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								euler375();
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
											2020-11-27 19:02:05 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								# --solutions--
  
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								// solution required
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								```