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

My friend was considering relatively simple case - 8 colors, no repeats, no blanks.

With no repeats, there's no need for the max entropy consideration, all guesses have the same entropy and first or random guessing all work fine.

Here's the full code to solve that variant:

# SET UP
import random
import itertools
colors = ('red', 'orange', 'yellow', 'green', 'blue', 'indigo', 'violet', 'ultra')

# ONE FUNCTION REQUIRED
def EvaluateCode(guess, secret_code):
    key = []
    for i in range(0, 4):
        for j in range(0, 4):
            if guess[i] == secret_code[j]:
                key += ['black'] if i == j else ['white']    
    return key

# MAIN CODE
# choose secret code
secret_code = random.sample(colors, 4)
print ('(shh - secret code is: ', secret_code, ')\n', sep='')
# create the full list of permutations
full_code_list = list(itertools.permutations(colors, 4))
N_guess = 0
while True:
    N_guess += 1
    print ('Attempt #', N_guess, '\n-----------', sep='')
    # make a random guess
    guess = random.choice(full_code_list)
    print ('guess:', guess)
    # evaluate the guess and get the key
    key = EvaluateCode(guess, secret_code)
    print ('key:', key)
    if key == ['black', 'black', 'black', 'black']:
        break
    # remove codes from the code list that don't match the key
    full_code_list2 = []
    for i in range(0, len(full_code_list)):
        if EvaluateCode(guess, full_code_list[i]) == key:
            full_code_list2 += [full_code_list[i]]
    full_code_list = full_code_list2
    print ('N remaining: ', len(full_code_list), '\n', full_code_list, '\n', sep='')
print ('\nMATCH after', N_guess, 'guesses\n')