There is a 3-digit code to open a lock. There are four 3-digit numbers...
Without the hints, there are 1000 possible 3-digit codes (from 000 to 999). However, with the hints, we can eliminate some of these possibilities.
Let's look at the hints:
1. "One digit is correct and in its place" for the number 839.
2. "One digit is correct but in the wrong place" for the number 854.
3. "Two digits are correct but in the wrong place" for the number 369.
4. "Nothing is correct" for the number 721.
Using these hints, we can narrow down the possibilities.
For hint 1, we know that one of the digits in the code is an 8, 3, or 9. We also know that it's in the correct place. So the code must be one of the following:
- 8 _ _
- _ 3 _
- _ _ 9
For hint 2, we know that one of the digits in the code is a 5, 4, or 8. We also know that it's in the code, but in the wrong place. So the code must be one of the following:
- _ 5 _
- 4 _ _
- _ _ 8
For hint 3, we know that two of the digits in the code are a 3, 6, or 9. We also know that they're in the code, but in the wrong place. So the code must be one of the following:
- 3 6 _
- 3 _ 9
- _ 6 9
For hint 4, we know that none of the digits in the code are a 7, 2, or 1. So the code can't be any of the following:
- 7 _ _
- _ 2 _
- _ _ 1
Putting all of this information together, we can eliminate a lot of possibilities. For example, we know that the code can't contain a 2 or a 7, so we can eliminate all codes that have a 2 or 7 in them.
Using this process of elimination, we can narrow down the possibilities until we find the code that fits all of the hints.
Here's the final list of possibilities:
- 839
- 369
- 936
Of these, only one fits all of the hints: 369.
Therefore, the code to open the lock is 369.
There is a 3-digit code to open a lock. There are four 3-digit numbers...

Correct code
