How to Find a Lock Combination

I sorted out my safe recently and decided that many papers and other items don't need to be in a safe. I saw a couple of Master padlocks there and wanted to keep them outside the safe. But I wanted to keep them only if I knew the combinations. I had a whole bunch of note papers with combinations on them and tried them out on the two locks. I quickly opened one of them, so I tagged it with its combination and put it away. But the other one would not open. So I threw it out.

I wondered about that. It's a perfectly good lock. The only reason why I want to throw it out is that I did not know its combination. Was there some way I could get that combination by fooling around with lock somehow? The existence of some way could endanger the security of the lock, but I wanted to do something other than throw it out.

I looked on the Web using Google and found Electroatomics. The site gave a procedure for finding the combination of a Master padlock. It's a good site, and is its owner's most favorite page. I looked through the instructions and it said to turn the lock to 0 (the numbers range from the real numbers 0 through 40, but combinations are given in integers). So I did that. Then it said to pull on the hasp and turn the dial. Which direction? It did not say. I turned it towards the forward numbers, 1, 2, and so forth. But how can I when the hasp was pulled? After some monkeying around I found that I could hop from stable "settle" point to point. The instructions say to move the dial of the lock until it hits these points and record them. They say there should be 12 of them. I tried that and got a series of numbers. They could be right on the integers, as 13, or they could be in between, like between 18 and 19. In that case record an 18.5.

He then says that there should be seven numbers ending in .5. He says these are decoys. He says look at the numbers that end in .0; i.e., integers. There should be five of these. In his example, he said he got 32, 22, 19, 12, and 2. They all end in the same digit except one. That one is the third number of the combination. So in his case, the lock's combination ended in a 19.

I tried that with the lock I had and got a series of numbers. But different times I did it, I got slightly different numbers, and I was getting 6, or 8, or something like that numbers ending in .5. The whole thing was wishy washy to me, and the integers I got had at least two repetitions of two integers, so I could not identify the third number of the combination. I reread the instructions and it said to turn it back and forth to see what range of numbers it would go in. He said if it went between 4.5 and 5.5, record a 4, and if it went between 4 and 5, record 4.5. I was not getting just exact readings and .5s however. I was also getting .8s and .3s and other such stuff. So the whole thing became really confusing. I put these results in a table, where left is as far left as I can get the stop point, and right is as far right. Avg is simply the average of those two numbers:

	Left	Right	Avg
1	-0.5	0.5	0
2	2.8	3.8	3.3
3	6.0	7.0	6.5
4	9.8	10.8	10.3
5	12.8	13.8	13.3
6	16.0	17.0	16.5
7	19.6	20.5	20.05
8	22.8	23.8	23.3
9	26.0	27.0	26.5
10	29.5	30.5	30.0
11	32.8	33.8	33.3
12	36.0	37.0	36.5

This still did not tell me much. I tabulated the 0s, the .3s, and the .5s, and got 3, 5, and 4 readings respectively. This did not match at all what Liam Bowen said I would get. I looked at the readings. The five .3s gave me 3, 10, 13, 23, 33, which according to Bowen's rules would say that 10 was the third number of the combination. But these are .3s, not integers. I noticed that the .5s gave 6, 16, 26, and 36, so that there is more than one sequence of numbers all ending in the same digit. So I tried something different. I rearranged the numbers into a 3x4 array:

0	3.3	6.5
10.3	13.3	16.5
20.05	23.3	26.5
30	33.3	36.5

Now it comes out. Each column looks like it lines up nicely except the first, where the 10.3 sticks out like a sore thumb. I was now certain that the third digit of the combination was 10.

I tried this out on a lock whose combination I knew. The combination ended in a 27. I tried the same table technique and, sure enough, the 27 was different from the others.

So that now I know the third number is a 10, Bowen then makes a lengthy explanation of what "mod 4" means. What he says is that that x - z = 0 mod 4, and that x - y = 2 mod 4, where the combination is x-y-z. This means the first number is one of 2, 6, 10, and so forth, and the second number is one of 0, 4, 8, and so forth. So now there are only 100 combinations to try.

I tried them one at a time, and none of them worked. Just as I was about to exhaust all the combinations, I pulled on the hasp. It unlocked! I had found it! I memorized the number (of course I won't give the result here as it would compromise the lock). But I had found the combination and now don't have to throw the lock out.

So the procedure for finding the combination of a Master Lock (it has to be a Master, according to Bowen) is:

1. Turn the dial while pulling the hasp out. There should be 12 points at which it "settles" (Bowen calls them "clicks").

2. At each point, turn the dial back and forth until it won't go and record the results to one-decimal accuracy. The result should be a table giving 12 left and right readings.

3. Take the average of each row of this table.

4. Rearrange these averages into a 3x4 table, putting 3 readings in the first row, 3 in the second and so forth.

5. Find the number whose decimal does not jibe with the other entries in its column. This number is the third number of the combination. Call this z. Call the combination x-y-z

6. Test all combinations of values of x and y, where x is congruent to z mod 4, and y+2 or y - 2 is congruent to z mod 4.

7. One of these should be the lock's combination. If this does not work, you made an error somewhere or they have manufactured a new type of lock.