| Subject: | wrong statement on mastermind page |
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| Date: | Tue, 23 Oct 2001 23:04:56 +0200 |
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| From: | Stephan Rafler |
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thank you for your superb mastermind page. there you state that with the strategy of consistent guesses one needs in the worst case 7 guesses. SLIGHTLY underestimated i would say. here is a sequence of 10 consistent guesses:
| 1 | | 5555 | | 0,0 | | 1296 |
| 2 | | 2201 | | 1,1 | | 625 |
| 3 | | 4104 | | 1,1 | | 120 |
| 4 | | 1303 | | 1,1 | | 20 |
| 5 | | 3402 | | 0,3 | | 6 |
| 6 | | 4213 | | 1,3 | | 5 |
| 7 | | 2314 | | 1,3 | | 4 |
| 8 | | 4321 | | 0,4 | | 3 |
| 9 | | 2143 | | 0,4 | | 2 |
| 10 | | 1234 | | 4,0 | | 1 |
the number to the right is the number of consistent guesses one could make at that stage. my computer found 2-10 after about 10,000,000 random games. i added the 5555 with a slight grin on my lips. i wouldn't bet that there is no sequence with 11. in fact it would be an interesting task to show that there is none above a certain number. in some way you are right that 7 is the worst case: because the higher ones become "better" again!
stephan
Copyright © 1996-2008 Alexander Bogomolny
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