Guess the Number

4321

There are a couple of ways to deduce the answer, but the quickest way is:

1. Since there are 6 guesses and only 4 digits, that means there must be 2 guesses with the same correct digit as 2 other guesses. There are only 4 possibilities:
   • First digit is 6
   • Second digit is 3
   • Third digit is 2
   • Last digit is 8
2. But we know that every guess has exactly one correct digit, and therefore has three incorrect digits.
   • If 6 were correct, 6358 and 6728 would mean 3, 2, and 8 were all incorrect, which contradicts our finding above.
   • If 8 were correct, the same two guesses result in a similar contradiction.
   • Therefore 6 and 8 are incorrect, and 3 and 2 are correct.
3. Since 3 and 2 are correct, we have already identified the correct digit in these guesses: 6358, 9306, 6728, 5627. We have 4882 and 1191 left to work with.
4. The correct digit in 4882 must be 4, because the second and third digits have already been identified and 2 has already been used (remember that all the digits are different).
5. Finally, there is only one unidentified digit left, the last digit, and it must be 1 so that 1191 has a correct digit. So the answer is 4321.