optimal strategy for 5 pegs, 7 colors-mastermind

[Michael Hürter]

I had solved this a long time ago,
had computed the optimal strategies and had proven
that no better strategies exist.
(2002 I had printed the optimal strategy tables on paper).

I present here some results:

An optimal strategy for the 5 pegs, 7 colors-mastermind
requires 85645 moves: 85645 / 16807 : 5,09579

In the 5 pegs, 7 colors-mastermind the codebreaker can solve the pattern
in 6 moves or fewer (planning to publish a prove of this at my homepage).

The best strategies in the 5 pegs, 7-colors-mastermind with 6 moves or fewer
require 85656 moves.

An optimal strategy for the 5 pegs, 6 colors-mastermind
requires 36721 moves.

An optimal strategy for the 5 pegs, 4 colors-mastermind
requires 3954 moves.

An optimal strategy for the 5 pegs, 5 colors-mastermind
requires 13496 moves.

In the 5 pegs, 8 colors-mastermind the codebreaker can solve the pattern
in 7 moves or fewer (this result is trivial).

In the 5 pegs, 9 colors-mastermind the codebreaker can solve the pattern
in 7 moves or fewer.

In the 4 pegs, 10 digits-bulls and cows the codebreaker can't solve the pattern
in 6 moves or fewer. (5040 possibilities and 7 moves required)

In the 5 pegs, 10 digit-bulls and cows the codebreaker can solve the pattern
in 7 moves or fewer (30240 possibilities).

The first I solved was the 5 pegs, 3 colors-version for which
an optimal strategy requires 816 moves.

If the codebreaker can use another color, it is possible to
solve this in 815 moves.

This is not possible in the 5 pegs, 4 colors-version and in the 5 pegs, 5 colors-version.

By the way: I bought this in the 80's and according to the game description
the 4 pegs, 6 colors-version is for beginners (SH für Anfänger).

Michael Hürter

[James Dow Allen]

Michael Hürter <abcd4...@yahoo.de> might have writ, in news:2dfb22da-
b294-40fa-a39...@googlegroups.com:

> In the 5 pegs, 7 colors-mastermind the codebreaker can solve the pattern
> in 6 moves or fewer (planning to publish a prove of this at my homepage).

Yes, this is demonstrated by my Javascript:
http://fabpedigree.com/james/mmind/mmind.htm

I announced this result in rec.puzzles in 2011:

https://groups.google.com/group/rec.puzzles/browse_thread/thread/6cfb14279d
8cdfbb

... though much of the subsequent discussion focused on
picking 7 distinguishable colors for the color-blind.

James Dow Allen

[Pavel314]

We used to play this when my children were little. My son is partially color-blind and couldn't distinguish between two of the colors; I forget which after 30 years or so. I put a drop of white out on top of the pegs of one of the confusing colors so that he could tell which were which and he did quite well at the game.