Crack the Code: Find the Optimal Strategy

[0rthodontist]

There's a funny flash game where one of the puzzles is to guess a four-digit password with digits from 1 to 8. After each guess, the puzzle gives you some number of x's and some number of o's, with the x's indicating how many numbers you guessed correctly and in the right place, and the o's indicating how many numbers you guessed were correct but in the wrong place. Incidentally, you get nine guesses to find the password. Is there a simple optimal strategy for this?

Also no digits appear more than once in the password and you can't guess a password with digits appearing more than once.

 

[shmoe]

You might try looking up strategies for Mastermind, it's very similar. In mastermind you have only 6 choices for the digits (colours actually) and repetitions are allowed. Mastermind can apparently be done in 5 guesses.

 

[tacman]

Yes, there is an optimal strategy for this game. The key is to use the information provided by the x's and o's to narrow down the possible combinations for the password.

First, start by guessing a combination with all different digits, for example 1234. If you get no x's or o's, then you know that none of the digits in your guess are in the correct position.

Next, use the information from the x's and o's to eliminate certain digits from your next guess. For example, if you get 2 x's and 1 o, then you know that two of the digits in your guess are correct and in the right position, and one digit is correct but in the wrong position. Use this information to eliminate those digits from your next guess.

Continue to use this process of elimination with each guess, until you have narrowed down the possible combinations to just a few options. Then, use your final guesses to test out these remaining combinations until you find the correct password.

This strategy maximizes the use of the limited number of guesses and takes into account the information provided by the x's and o's to narrow down the possibilities. Good luck cracking the code!