| 
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 |  |  | --- | 
					
						
							|  |  |  | id: 5900f41e1000cf542c50ff31 | 
					
						
							|  |  |  | title: 'Problem 178: Step Numbers' | 
					
						
							| 
									
										
										
										
											2020-11-27 19:02:05 +01:00
										 |  |  | challengeType: 5 | 
					
						
							| 
									
										
										
										
											2019-08-05 09:17:33 -07:00
										 |  |  | forumTopicId: 301813 | 
					
						
							| 
									
										
										
										
											2021-01-13 03:31:00 +01:00
										 |  |  | dashedName: problem-178-step-numbers | 
					
						
							| 
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 |  |  | --- | 
					
						
							|  |  |  | 
 | 
					
						
							| 
									
										
										
										
											2020-11-27 19:02:05 +01:00
										 |  |  | # --description--
 | 
					
						
							|  |  |  | 
 | 
					
						
							| 
									
										
										
										
											2018-10-08 01:01:53 +01:00
										 |  |  | Consider the number 45656. | 
					
						
							| 
									
										
										
										
											2020-11-27 19:02:05 +01:00
										 |  |  | 
 | 
					
						
							| 
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 |  |  | It can be seen that each pair of consecutive digits of 45656 has a difference of one. | 
					
						
							|  |  |  | 
 | 
					
						
							| 
									
										
										
										
											2020-11-27 19:02:05 +01:00
										 |  |  | A number for which every pair of consecutive digits has a difference of one is called a step number. | 
					
						
							| 
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 |  |  | 
 | 
					
						
							| 
									
										
										
										
											2020-11-27 19:02:05 +01:00
										 |  |  | A pandigital number contains every decimal digit from 0 to 9 at least once. | 
					
						
							| 
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 |  |  | 
 | 
					
						
							| 
									
										
										
										
											2021-07-12 16:19:03 +02:00
										 |  |  | How many pandigital step numbers less than ${10}^{40}$ are there? | 
					
						
							| 
									
										
										
										
											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
										 |  |  | 
 | 
					
						
							| 
									
										
										
										
											2021-07-12 16:19:03 +02:00
										 |  |  | `stepNumbers()` should return `126461847755`. | 
					
						
							| 
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 |  |  | 
 | 
					
						
							| 
									
										
										
										
											2020-11-27 19:02:05 +01:00
										 |  |  | ```js | 
					
						
							| 
									
										
										
										
											2021-07-12 16:19:03 +02:00
										 |  |  | assert.strictEqual(stepNumbers(), 126461847755); | 
					
						
							| 
									
										
										
										
											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 | 
					
						
							| 
									
										
										
										
											2021-07-12 16:19:03 +02:00
										 |  |  | function stepNumbers() { | 
					
						
							| 
									
										
										
										
											2020-09-15 09:57:40 -07:00
										 |  |  | 
 | 
					
						
							| 
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 |  |  |   return true; | 
					
						
							|  |  |  | } | 
					
						
							|  |  |  | 
 | 
					
						
							| 
									
										
										
										
											2021-07-12 16:19:03 +02:00
										 |  |  | stepNumbers(); | 
					
						
							| 
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 |  |  | ``` | 
					
						
							|  |  |  | 
 | 
					
						
							| 
									
										
										
										
											2020-11-27 19:02:05 +01:00
										 |  |  | # --solutions--
 | 
					
						
							| 
									
										
										
										
											2018-09-30 23:01:58 +01:00
										 |  |  | 
 | 
					
						
							|  |  |  | ```js | 
					
						
							|  |  |  | // solution required | 
					
						
							|  |  |  | ``` |