How to solve the “Mastermind” guessing game?

Question

How would you create an algorithm to solve the following puzzle, \"Mastermind\"?

Your opponent has chosen four different colours from a set of six (yellow, blue, gre

Answer 1

Here's a link to pure Python solver for Mastermind(tm): http://code.activestate.com/recipes/496907-mastermind-style-code-breaking/ It has a simple version, a way to experiment with various guessing strategies, performance measurement, and an optional C accelerator.

The core of the recipe is short and sweet:

import random
from itertools import izip, imap

digits = 4
fmt = '%0' + str(digits) + 'd'
searchspace = tuple([tuple(map(int,fmt % i)) for i in range(0,10**digits)])

def compare(a, b, imap=imap, sum=sum, izip=izip, min=min):
    count1 = [0] * 10
    count2 = [0] * 10
    strikes = 0
    for dig1, dig2 in izip(a,b):
        if dig1 == dig2:
            strikes += 1
        count1[dig1] += 1
        count2[dig2] += 1
    balls = sum(imap(min, count1, count2)) - strikes
    return (strikes, balls)

def rungame(target, strategy, verbose=True, maxtries=15):
    possibles = list(searchspace)
    for i in xrange(maxtries):
        g = strategy(i, possibles)
        if verbose:
            print "Out of %7d possibilities.  I'll guess %r" % (len(possibles), g),
        score = compare(g, target)
        if verbose:
            print ' ---> ', score
        if score[0] == digits:
            if verbose:
                print "That's it.  After %d tries, I won." % (i+1,)
            break
        possibles = [n for n in possibles if compare(g, n) == score]
    return i+1

def strategy_allrand(i, possibles):
    return random.choice(possibles)

if __name__ == '__main__':
    hidden_code = random.choice(searchspace)
    rungame(hidden_code, strategy_allrand)

Here is what the output looks like:

Out of   10000 possibilities.  I'll guess (6, 4, 0, 9)  --->  (1, 0)
Out of    1372 possibilities.  I'll guess (7, 4, 5, 8)  --->  (1, 1)
Out of     204 possibilities.  I'll guess (1, 4, 2, 7)  --->  (2, 1)
Out of      11 possibilities.  I'll guess (1, 4, 7, 1)  --->  (3, 0)
Out of       2 possibilities.  I'll guess (1, 4, 7, 4)  --->  (4, 0)
That's it.  After 5 tries, I won.