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 ...

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!

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 (197677) showed that the codebreaker can always succeed in
five or fewer moves (i.e., knows the code after four guesses)."
wes

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 (197677) 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...???

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 (197677) 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