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

To work out the "worst" case, instead of using entropic I am looking to the partition that has the maximum number of elements, then select the try that is a minimum for this maximum => This will give me the minimum number of remaining possibility when I am not lucky (which happens in the worst case).

This always solve standard case in 5 attempts, but it is not a full proof that 5 attempts are really needed because it could happen that for next step a bigger set possibilities would have given a better result than a smaller one (because easier to distinguish between).

Though for the "Standard game" with 1680 I have a simple formal proof: For the first step the try that gives the minimum for the partition with the maximum number is 0,0,1,1: 256. Playing 0,0,1,2 is not as good: 276. For each subsequent try there are 14 outcomes (1 not placed and 3 placed is impossible) and 4 placed is giving a partition of 1. This means that in the best case (all partition same size) we will get a maximum partition that is a minimum of (number of possibilities - 1)/13 (rounded up because we have integer so necessarily some will be less and other more, so that the maximum is rounded up).

If I apply this:

After first play (0,0,1,1) I am getting 256 left.

After second try: 20 = (256-1)/13

After third try : 2 = (20-1)/13

Then I have no choice but to try one of the two left for the 4th try.

If I am unlucky a fifth try is needed.

This proves we need at least 5 tries (but not that this is enough).