Calculation Request...???
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From: TranslucentAmoebae on 11 Apr 2008 19:59 i have a ( Game ) Mastermind on my Mac, and some time ago, i wrote a version for my HP48... And it seems to me that i win too easily. ( usually 8 ± guesses ) How many guesses should a perfectly logical approach require for 6 holes with 13 colours? ( Reminder ) The Game will tell you how many colors are right or how many colors are in the correct positions, But Not Which specific holes/colors are correct. Thanx!
From: Wes on 12 Apr 2008 11:37 On Apr 12, 2:59 am, TranslucentAmoebae <transamoe...(a)seanet.com> wrote: > i have a ( Game ) Mastermind on my Mac, and some time ago, i wrote a > version for my HP48... > And it seems to me that i win too easily. ( usually 8 ± guesses ) > > How many guesses should a perfectly logical approach require for 6 > holes with 13 colours? Did you mean 6 colors and 13 rows of holes? My children's Mastermind has 10 rows of holes. The picture in the Wikipedia article shows 12 rows. http://en.wikipedia.org/wiki/Mastermind_%28board_game%29 http://mathworld.wolfram.com/Mastermind.html states: "Knuth (1976-77) showed that the codebreaker can always succeed in five or fewer moves (i.e., knows the code after four guesses)." -wes
From: TranslucentAmoebae on 16 Apr 2008 15:15 On Apr 12, 8:37 am, Wes <wjltemp...(a)yahoo.com> wrote: > On Apr 12, 2:59 am, TranslucentAmoebae <transamoe...(a)seanet.com> > wrote: > > > i have a ( Game ) Mastermind on my Mac, and some time ago, i wrote a > > version for my HP48... > > And it seems to me that i win too easily. ( usually 8 ± guesses ) > > > How many guesses should a perfectly logical approach require for 6 > > holes with 13 colours? > > Did you mean 6 colors and 13 rows of holes? My children's Mastermind > has 10 rows of holes. The picture in the Wikipedia article shows 12 > rows.http://en.wikipedia.org/wiki/Mastermind_%28board_game%29 > > http://mathworld.wolfram.com/Mastermind.htmlstates: > "Knuth (1976-77) showed that the codebreaker can always succeed in > five or fewer moves (i.e., knows the code after four guesses)." > > -wes This Version that i have: SMasterMind v.1.2.4 ©2006 Th. Robisson and Ph. Galmel that i got from a MacWorld CD Has what may be an anomalous arrangement of 6 holes and 12 colors, Plus Holes themselves may be part of the solution, effectively making for 13 colors. My approach has been to try sets of colors first to determine which colors are used; AABBCC DDEEFF ... Until i get 6 Hits. Then Try rearranging them, working from a base of consistency as i go... It seems to me that of the zillions of combinations, 8 guesses is far too few to find the solution. Am i a Jedi...???
From: Irl on 23 Apr 2008 06:27
On Apr 16, 3:15 pm, TranslucentAmoebae <transamoe...(a)seanet.com> wrote: > On Apr 12, 8:37 am, Wes <wjltemp...(a)yahoo.com> wrote: > > > > > On Apr 12, 2:59 am, TranslucentAmoebae <transamoe...(a)seanet.com> > > wrote: > > > > i have a ( Game ) Mastermind on my Mac, and some time ago, i wrote a > > > version for my HP48... > > > And it seems to me that i win too easily. ( usually 8 ± guesses ) > > > > How many guesses should a perfectly logical approach require for 6 > > > holes with 13 colours? > > > Did you mean 6 colors and 13 rows of holes? My children's Mastermind > > has 10 rows of holes. The picture in the Wikipedia article shows 12 > > rows.http://en.wikipedia.org/wiki/Mastermind_%28board_game%29 > > >http://mathworld.wolfram.com/Mastermind.htmlstates: > > "Knuth (1976-77) showed that the codebreaker can always succeed in > > five or fewer moves (i.e., knows the code after four guesses)." > > > -wes > > This Version that i have: > SMasterMind v.1.2.4 ©2006 Th. Robisson and Ph. Galmel > that i got from a MacWorld CD > Has what may be an anomalous arrangement of 6 holes and 12 colors, > Plus Holes themselves may be part of the solution, effectively making > for 13 colors. > > My approach has been to try sets of colors first to determine which > colors are used; AABBCC DDEEFF ... > Until i get 6 Hits. Then Try rearranging them, working from a base of > consistency as i go... > It seems to me that of the zillions of combinations, 8 guesses is far > too few to find the solution. > > Am i a Jedi...??? I'm assuming it's 6 colors; the number of rows is irrelevant as long as it's enough to allow solving the problem. I'm also assuming, as is usually true, that each row contains 4 holes. Thus there are a total of 7^4 = 2401 possible states. The possible answers are (B = black response meaning one of your guess pegs is the right color in the right position; W = white meaning one is the right color but wrong position) BBBB (you win) BBWW (can't have just BBBW because the 4th one has no place to be except right) BBW BB BWWW BWW BW B WWWW WWW WW W nothing So each guess gives one of 13 responses. Thus you can in principle reduce the number of possibilities by a factor of 13 per guess. After 1 guess, you have at least 2401/13 = 185 possibilities; after 2, at least 15; after 3, at least 2; after 4, at least 1. So four guesses might be enough. Routinely getting it in 6 is to be expected if you have a good strategy. Of course, with a bad strategy you might never get it: if you just keep asking the same question the number of possibilities does not decrease below the initial 185. I haven't played in a while but I recall that some such number was about what I usually did. This analysis is pretty crude, of course; the actual reduction in the pool of possibilities depends on the guess, but leaving aside "dumb luck", i.e. just guessing right the first time, it suggests that an optimal strategy should not be expected to get you there in fewer than 4 guesses. Irl |