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 <transamoe...@seanet.com>

wrote:[color=blue]

> 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?[/color]

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.

[url]http://en.wikipedia.org/wiki/Mastermind_%28board_game%29[/url]

[url]http://mathworld.wolfram.com/Mastermind.html[/url] 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

Re: Calculation Request...???

On Apr 12, 8:37 am, Wes <wjltemp...@yahoo.com> wrote:[color=blue]

> On Apr 12, 2:59 am, TranslucentAmoebae <transamoe...@seanet.com>

> wrote:

>[color=green]

> > 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 )[/color]

>[color=green]

> > How many guesses should a perfectly logical approach require for 6

> > holes with 13 colours?[/color]

>

> 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.[url]http://en.wikipedia.org/wiki/Mastermind_%28board_game%29[/url]

>

> [url]http://mathworld.wolfram.com/Mastermind.htmlstates:[/url]

> "Knuth (1976-77) showed that the codebreaker can always succeed in

> five or fewer moves (i.e., knows the code after four guesses)."

>

> -wes[/color]

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 <transamoe...@seanet.com>

wrote:[color=blue]

> On Apr 12, 8:37 am, Wes <wjltemp...@yahoo.com> wrote:

>

>

>[color=green]

> > On Apr 12, 2:59 am, TranslucentAmoebae <transamoe...@seanet.com>

> > wrote:[/color]

>[color=green][color=darkred]

> > > 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 )[/color][/color]

>[color=green][color=darkred]

> > > How many guesses should a perfectly logical approach require for 6

> > > holes with 13 colours?[/color][/color]

>[color=green]

> > 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.[url]http://en.wikipedia.org/wiki/Mastermind_%28board_game%29[/url][/color]

>[color=green]

> >[url]http://mathworld.wolfram.com/Mastermind.htmlstates:[/url]

> > "Knuth (1976-77) showed that the codebreaker can always succeed in

> > five or fewer moves (i.e., knows the code after four guesses)."[/color]

>[color=green]

> > -wes[/color]

>

> 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...???[/color]

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