All,
I just came across a game called Bagels. Even though there are 648 possible starting numbers with those rules, you can come up with a strategy that will determine the solution without too many guesses. Having worked out such a strategy, I wondered if it was optimal. It is Friday after lunch and my brain has checked out for the weekend so I figured I would ask you monks and have a little fun in the process.

That means I am changing the rules.

• No restriction on first position
• Values not restricted to 0-9 (we will limit it to a maximum of 36 using 0-9 and A-Z)
• Number of positions not limited to 3 (no more than say 10)
• Guesses must meet the same burden as the picked number (no repeats)

So your challenge is to devise a strategy that, given the input conditions (number of positions and maximum possible value), produces a solution with the optimal number of guesses. Here is an example:

perl bagel_solver.pl p=4 v=14 s=1ACE
[download]

p is for the number of positions. v is for the maximum value 14 = 0-9, A, B, C, D, E. s is for the solution. The program will obviously play alone and not interactively.

Given the new rules, I am not sure if my strategy will still work so I post some time this weekend after I have had a chance to think about it. Until then, enjoy those bagels.

See also Mastermind.

Update: In the CB, MidLifeXis has pointed out that I have left a lot to be desired in how to choose a winner (scoring solutions) as well as restricting the input to command line arguments making a test harness prohibitive. I will be offline for much of the weekend and MidLifeXis has graciously agreed to take over explaining how those issues will be resolved :-)

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