How to Solve Combination Lock Puzzles

Combination Lock, also called Crack the Code, is a deduction puzzle similar to the game Mastermind. However, instead of colored pegs, you are trying to solve a number code, usually from 3 to 5 digits.

You are given a set of attempts matching the length of the code you will be solving, and are told with each attempt whether any of the digits are part of the correct combination, and whether they are in the correct position. Typically with numeric codes like this, it is assumed that the digits will all be different numbers.

For our puzzles, rather than using text beneath each clue, we will use circles for shorthand.

If all circles are hollow, none of the digits are in the combination.
A gray circle means that a digit is correct, but in the wrong position.
And a solid black circle means that a digit is correct and in the right position.

Now, let’s look at all the clues for our example puzzle.

With most puzzles, it is usually best to begin with an attempt that had nothing correct, because it will help you eliminate digits in other attempts. However, in this case, none of the numbers from 4-1-2 appear in any other combination.

Instead, let us consider the attempts for 7-0-9, which has one digit in the correct position, and 0-8-7, which has two correct digits, but both in the wrong position. Each of these attempts contains both 0 and 7. Because of the clue for 7-0-9, we know that only one of them is in the correct combination, not both. Since we know there are two correct digits in 0-8-7, we can deduce that the 8 is the other correct number, and that it is not placed in the middle.

So now, we can come back to the attempt of 5-6-8. We know that 8 is a correct digit, and that it doesn’t go in the middle of the combination. Here, there is only one correct digit, which must be the 8, and it is not the third digit, so that means that 8 must be the first digit.

Next, we look again at 7-0-9. From our earlier deduction, we know that either 7 or 0 is correct, but not both. And we now know that 8 must be the first digit. because the correct number in this attempt is in the correct position, according to the clue, the 7 cannot be correct, because that is where the 8 will go.

Therefore, the first two digits are 8-0, and we’re just looking for the third.

So we come back to the final clue, 3-9-7. We know that neither 9 or 7 are in the code, because 0 was the only correct digit in 7-0-9, as we just learned. This means 3 is the correct digit, and the only position left in our combination is the third digit.