| 
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 |  |  | --- | 
					
						
							|  |  |  | id: 5900f4e11000cf542c50fff3 | 
					
						
							|  |  |  | title: 'Problem 372: Pencils of rays' | 
					
						
							| 
									
										
										
										
											2020-11-27 19:02:05 +01:00
										 |  |  | challengeType: 5 | 
					
						
							| 
									
										
										
										
											2019-08-05 09:17:33 -07:00
										 |  |  | forumTopicId: 302034 | 
					
						
							| 
									
										
										
										
											2021-01-13 03:31:00 +01:00
										 |  |  | dashedName: problem-372-pencils-of-rays | 
					
						
							| 
									
										
										
										
											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
										 |  |  | 
 | 
					
						
							| 
									
										
										
										
											2020-11-27 19:02:05 +01:00
										 |  |  | Let R(M, N) be the number of lattice points (x, y) which satisfy M | 
					
						
							| 
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 |  |  | 
 | 
					
						
							| 
									
										
										
										
											2020-11-27 19:02:05 +01:00
										 |  |  | Note: represents the floor function. | 
					
						
							| 
									
										
										
										
											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
										 |  |  | `euler372()` should return 301450082318807040. | 
					
						
							| 
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 |  |  | 
 | 
					
						
							| 
									
										
										
										
											2020-11-27 19:02:05 +01:00
										 |  |  | ```js | 
					
						
							|  |  |  | assert.strictEqual(euler372(), 301450082318807040); | 
					
						
							| 
									
										
										
										
											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 euler372() { | 
					
						
							| 
									
										
										
										
											2020-09-15 09:57:40 -07:00
										 |  |  | 
 | 
					
						
							| 
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 |  |  |   return true; | 
					
						
							|  |  |  | } | 
					
						
							|  |  |  | 
 | 
					
						
							|  |  |  | euler372(); | 
					
						
							|  |  |  | ``` | 
					
						
							|  |  |  | 
 | 
					
						
							| 
									
										
										
										
											2020-11-27 19:02:05 +01:00
										 |  |  | # --solutions--
 | 
					
						
							| 
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 |  |  | 
 | 
					
						
							|  |  |  | ```js | 
					
						
							|  |  |  | // solution required | 
					
						
							|  |  |  | ``` |