How Many Possible Combinations of 3 Numbers Are There?

If each digit in a 3-digit lock comprises the digits 0 through 9, then each dial can be adjusted to one of 10 possible combinations (0, 1, 2, 3, 4, 5, 6, 7, 8 or 9). Therefore, there are 1,000 distinct viable combinations. Three-digit padlocks are still extensively used for locking bicycles, baggage, and securing storage sheds.

More digits result in more combinations. With 40-digit combination locks, such as those usually seen on lockers, things become more problematic. The basic Master Lock, for instance, has 64,000 possible combinations. So, let’s examine the probabilities of breaking each sort of lock.

3-Digit Combinations for Locks

Despite the fact that 3-digit padlocks have 1,000 possible combinations, it is possible to open them without knowing the code. The trick to breaking them, fortunately, has little to do with attempting hundreds of different number combinations. Mastering the small differences in the feel of the lock as you scroll through the different numbers is more important.

To test it for yourself, acquire a padlock whose combination you know and follow the procedures below:

The ability to continuously apply sufficient force to lift the shackle upwards is one of the most important aspects of picking these types of locks (the hook-shaped part of the lock). Pull the shackle away from the lock body in the same manner as if you were opening the lock.
The easiest method is to link the lock to a solid item so that the lock body can be pulled down.
Beginning with the bottom row of numerals, while maintaining upward pressure on the lock lever, scroll through each one.
When the correct number is selected, you should hear a tiny click. You can also feel the internal wheel “fall into place” with sufficient repetition, making the dial slightly more difficult to move.
After determining the first accurate number, proceed to the next dial and repeat the process.
You will repeat the process with the third dial, but it will be easy to determine when you’ve reached the correct number since the lock will open.
How to Determine the Combination of a Lock
It is possible, with enough practise, to crack combination locks, such as a typical 40-digit Master Lock, without knowing the correct combination. The key of opening a combination lock without the combination resides mostly on exerting upward pressure to the shackle at the correct angle.

As with a padlock, you can either attach the combination lock to a sturdy object (advised only if you know the combination) or gently lift it using your left index or middle finger. If you pull up with excessive force, the number dial will not move. However, if you do not pull up with sufficient force, the dial will spin freely without disclosing much information.

The secret? Obtain the proper equilibrium between the two extremes. To determine the combination, try the steps below:

Zero out the lock’s value.

Continue putting just enough upward pressure on the shackle to gradually separate it from the lock’s body.
Start turning the dial in the clockwise direction until you hear a slight click or feel resistance as the lock catches at a specific number. Turn the dial many times to ensure that the shackle pressure is accurate. If you experience resistance every few numbers, you are applying too much upward force.
When the pressure is correct, you should observe that the lock captures only one number every full turn.
Add 5 to the amount of receptions made consistently. This is the initial digit in the combination.
Beginning with the first number, spin the shackle counterclockwise while maintaining the same pressure.
After completing one full round, pay particular attention to the second number as you feel for it.
The lock may bump somewhat as you turn it, but eventually you’ll reach a number that generates far more resistance, making it difficult to continue turning. This is the second number of your combo.
Then, simply turn the dial counterclockwise until the shackle releases and unlocks, which will certainly occur when you land on the third digit.
How to Determine How Many Possible Combinations There Are
Permutation is a mathematical concept that can be utilised to determine the number of possible possibilities for any given lock. Permutation specifies the number of possible arrangements for a given collection of variables (in this case, numbers).

One version of permutation formula permits repetition, whereas the other does not. Because the same number could be used twice in a combination, we will apply the first type of formula for combination locks. For instance, the combination of a lock could be 9, 3, 9.

The formula to determine the numerous potential combinations is as follows: Nr. The characters in this equation represent:

N = the total number of variables (in this case numbers) from which to select. r = the number of “N” from which to select.
To illustrate how this formula works, consider a 3-digit padlock with three dials, each of which contains the digits 0 through 9. N = 10 because there are a total of 10 numbers from which to choose.

We must correctly place each of these ten numbers three times, so r equals three. Putting these figures into our formula, we obtain:

103 = 1,000
This means that our 3-digit lock has 1,000 possible combinations. In the case of a 40-digit combination lock, we could use the same formula and simply rewrite it to account for the 40 possible dial combinations. Since we must select the best option three times, our formula would read:

403 = 64,000
This is how we arrive at the conclusion that a combination lock has 64,000 possible solutions. Fortunately, we now know a few tricks that allow us to open both types of locks without manually or aimlessly trying every possible combination.