Glider's Masterlock Cracker

The mechanism of the Masterlock brand combination locks is designed such that it is possible to manipulate the lock in just a few moments and eliminate 63,900 of the 64,000 possible combinations. This leaves just 100 possible combinations to test on the lock. While this is still much slower than simply cutting the lock off. Manipulating a combination is really only useful when there is a pressing need to be able to reuse a lock.

Masterlock padlocks will freeze up the dial when pressure is applied to the shackle of the lock. Careful inspection of the lock will reveal that the dial will freeze in twelve distinct positions. Seven of these positions will be with the number pointer between two numbers, and these can be discarded. Of the remaining five positions, the pointer will point directly to numbers on the dial face and 4 of the numbers will end with the same digit. (For those math freaks out there, four of the five will possess the same modulo 10.) For instance the five numbers that the dial will freeze on may be 1, 11, 21, 31, and 4. We discard the 1, 11, 21, and 31 and are left with 4. We now know the last number of the three number combination, 4. We now have gone from 64,000 possible combinations to 1,600 possible combinations.

Now a bit of information about the way Masterlock codes combinations comes in handy. The first and last digits of the combination have the same remainder when divided by 4. In the example above the last digit is 4, and 4 divided by four is 1 with a remainder of 0. The first digit must then have a remainder of 0 when divided by 4. A master lock has the digits 0 through 39 on its dial, and thus in the example above ten numbers, 0, 4, 8, 12, 16, 20, 24, 28, 32, and 36 are left as possibilities for the first number. This reduces the total possible number of valid combinations to 400.

When divided by 4, the middle number has a remainder that differs by 2 from the remainder of the last number. Thus if the remainder of the last number in the combination is 0, the remainder of the middle number will be 2. If the last number divided by 4 leaves a remainder of 1, then the middle number will leave a remainder of 3. A remainder of 2 for the last number yields a remiander of 0 for the middle number, and a remainder of 3 on the last number yields a remainder of 1 for the middle number. This allows us to reduce the possibilities for the middle number to ten choices, in much the same way as we did for the first number. In the example we've given that would leave 2, 6, 10, 14, 18, 22, 26, 30, 34, and 38. The total possible valid combinations has now been reduced to 100.

I understand that although this algorithm is fairly simple, some people may not have the time to sort it out. For your convenience this page can take the last digit of the combination, which you must manipulate from the lock as described above, and provide you with a table of all the possible valid combinations. The table for the example above looks like this: