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| Thread ID: 66930 | 2006-03-11 21:54:00 | Sunday problem | Dally (6292) | PC World Chat |
| Post ID | Timestamp | Content | User | ||
| 437487 | 2006-03-11 21:54:00 | Awhile back someone posted a Sunday problem so I'll add another A school has 1000 students and 1000 lockers . The lockers are all in a row and start out closed. The first student walks down the row and opens each locker. The second student closes each even numbered locker. The third student approaches every third locker and changes its state. If it is open she closes it and if it is closed she opens it. The fourth student does the same to every fourth locker and so on. After all 1000 students have passed down the line how many lockers remain open? |
Dally (6292) | ||
| 437488 | 2006-03-11 22:27:00 | It's based on the "perfect square" solution from memory, and the highest locker number that fits as < 1,000 would be 31 squared = 961 So 31 remain open? Thats what my spreadsheet tells me anyway. |
godfather (25) | ||
| 437489 | 2006-03-11 23:16:00 | Well done. I think I'll have to come up with a more difficult question | Dally (6292) | ||
| 437490 | 2006-03-12 00:04:00 | Good effort GF. I ran a simulation using Access and there were indeed 31 lockers open, being lockers numbered 1, 4, 9, 25 etc - i.e the perfect squares. A |
andrew93 (249) | ||
| 437491 | 2006-03-12 00:36:00 | I thought it was going to be another illustration of infinity. A hotel has an infinite number of rooms. They are all occupied. A tour bus (carrying an infinite number of passengers) arrives. The manager doesn't panic. He just moves the present customers into the even numbered rooms. Then there is room for an infinite number of new customers in the odd numbered rooms. Try that one on your spreadsheet, GF. |
Graham L (2) | ||
| 437492 | 2006-03-12 01:15:00 | I thought it was going to be another illustration of infinity . A hotel has an infinite number of rooms . They are all occupied . A tour bus (carrying an infinite number of passengers) arrives . The manager doesn't panic . He just moves the present customers into the even numbered rooms . Then there is room for an infinite number of new customers in the odd numbered rooms . Try that one on your spreadsheet, GF . So you are saying that his hotel manager is infinitly rich? |
Greven (91) | ||
| 437493 | 2006-03-12 02:59:00 | And if the hotel manager is already infinitely rich, why would he need any help? | andrew93 (249) | ||
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