Bulls and Cows


Five games of the popular pencil-and-paper pastime "Bulls and Cows"* are shown below. These games were never completed, though, perhaps because at least one of the scoring boxes in each game is missing a single Bull or Cow. It is not known what caused the cattle to disappear, or how to address the problem.

*In Bulls and Cows, Player A determines a secret five-digit number. Digits from 0-9 may be used, and repeats are allowed. Player B attempts to determine the secret number by guessing his own five-digit string. Player A scores each guess by awarding a "Bull" for each correct digit in the correct position, or "Cow" for each correct digit in an incorrect position. A particular instance of a digit in a guess or in the answer cannot yield more than one Bull or Cow during a given guess, and a Bull will be awarded where possible -- thus, a guess/number of x3xxx against a number/guess of 33xxx yields one Bull (all of this subject to the unfortunate disappearance problem mentioned above).