Calculation Request...??? - Hewlett Packard

This is a discussion on Calculation Request...??? - Hewlett Packard ; 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 ...

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  1. Calculation Request...???

    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!

  2. Re: Calculation Request...???

    On Apr 12, 2:59 am, TranslucentAmoebae
    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/Masterm...8board_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

  3. Re: Calculation Request...???

    On Apr 12, 8:37 am, Wes wrote:
    > On Apr 12, 2:59 am, TranslucentAmoebae
    > 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/Masterm...8board_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...???

  4. Re: Calculation Request...???

    On Apr 16, 3:15 pm, TranslucentAmoebae
    wrote:
    > On Apr 12, 8:37 am, Wes wrote:
    >
    >
    >
    > > On Apr 12, 2:59 am, TranslucentAmoebae
    > > 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/Masterm...8board_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

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