Subject:	wrong statement on mastermind page
Date:	Tue, 23 Oct 2001 23:04:56 +0200
From:	Stephan Rafler

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

Mastermind

• Invitation To Mastermind
  • Random Strategy for Mastermind
• Mastermind: an interactive gizmo
• Computer Mastermind
• Mastermind Variants
• Bulls and Cows
• Vowel Movement
• Thugs and Bowmen

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