How Many Possible Combinations of 3 Numbers Are There?

Each dial of a 3-digit lock can be changed to one of ten possibilities if each digit contains the numbers 0 through 9. (0, 1, 2, 3, 4, 5, 6, 7, 8 or 9). That implies that there are 1,000 potential combinations in all. 3-digit padlocks are still frequently used in modern times for storage shed security, built-in baggage locks, and bike locks.

More combinations are possible with more digits. With 40-digit combination locks, like those frequently found on lockers, things become a little bit more difficult. For instance, there are 64,000 possible combinations for the typical Master Lock. Let’s examine the likelihood of picking each type of lock now.

Combinations for 3-Digit Locks

Even though 3-digit padlocks have 1,000 possible combinations, there are methods to access them without the combination. Fortunately, there isn’t much to be learned about them by attempting hundreds of different number combinations. It’s more an issue of getting used to how the lock feels when you scroll through the various numbers.

Take a padlock with a combination you are familiar with and perform the following actions to test it out for yourself:

Being able to continuously exert enough force to lift the shackle upward is one of the key strategies for picking these kinds of locks (the hook-shaped part of the lock). The same manner you would if you were opening the lock, you should pull the shackle away from the body of the lock.

To do this, the simplest method is to fasten the lock to a heavy item and then pull the lock body downward.

Scroll through each row of numbers starting with the bottom one while continuing to apply upward pressure on the lock handle.

You should hear a faint click when you land on the right number. Eventually, the inside wheel will “fall into place,” making the dial a little bit more difficult to spin.

Dial the second number and repeat the process after you’ve reached the first proper one.

With the third dial, you’ll follow the same procedure, although it’s a little simpler to know when you’ve reached the proper number because the lock should unlock.

Understanding Combination Locks

Without the correct combination, it can be a little more difficult to open combination locks, like a typical 40-digit Master Lock, but it is still achievable with enough effort. Applying just the appropriate amount of upward pressure on the shackle is essentially what will unlock a combination lock without the combination.

When using a combination lock, you have two options: you can either attach it to a solid object (only advised if you know the combination), or you can gently pull it upwards with your finger or thumb on the left hand.

The number dial won’t move at all if you apply too much pressure when pulling up. However, if you don’t pull up firmly enough, the dial will spin freely and disclose little.

The secret? Learn how to strike the right balance between the two extremes. Try the following to determine the combination:

Put the lock’s value at 0.

Just enough upward pressure must be maintained on the shackle to cause a gentle separation of the shackle from the lock body.

Start turning the dial counterclockwise when you feel resistance or hear a slight click when the lock catches at a particular number. To ensure that the pressure in your shackles is appropriate, turn the dial a few times. Note: If you encounter resistance after a few numbers, you’re pushing up too hard.

If the pressure is just right, you should observe that the lock only engages with one number for each complete rotation.

The number that consistently catches five more. That is the combination’s starting number.

Starting with the first number, rotate counterclockwise while continuing to squeeze the shackle firmly.

Pay close attention when you feel for the second number after doing one complete round.

As you crank the lock, it could jiggle a little bit, but ultimately you’ll hit a number that generates a lot more resistance, making it difficult to turn farther. Your second number in the combination is that one.

When you reach the third number, which is inevitable, the shackle will automatically release and unlock. From there, all you have to do is spin the dial counterclockwise once more.

How to Calculate the Number of Combinations Possible

You can use a mathematical concept called permutation to determine how many possible combinations there are for any lock. The term “permutation” refers to the variety of arrangements that can be made of a given collection of variables (in this case, integers).

Permutation formulae come in two flavours: ones that permit repetition and ones that don’t. In the case of a combination lock, we’ll use the first type of formula because the same number could be used twice in a combination. For illustration, the combination to a lock might be 9, 3, 9.

The formula to calculate all of the possible combinations is as follows: Nr. In this equation, the letters stand for:

N is the total number of available variables (in this case, numbers).

r is the number of “N” options available.

Let’s use the example of a 3-digit padlock with three dials that each have the options 0 through 9 to demonstrate how this formula functions. N is equal to 10 in this instance because there are a total of 10 possible numbers (0,1,2,3,4,5,6,7,8,9).

Since each of these 10 numerals must be appropriately positioned three times, r=3. When we enter those figures into our formula, we obtain:

103 = 1,000

This indicates that our 3-digit lock has 1,000 different possible combinations. In contrast, we could apply the same method and just modify it to take into account the 40 possible options for numbers on a 40-digit combination lock. Given that we must determine the right option three times, our formula would be as follows:

403 = 64,000

This is how we determine that there are 64,000 different ways to open a combination lock. Fortunately, we now have a few techniques that can open both sorts of locks without manually or randomly trying every conceivable combination.

Misha Khatri
Misha Khatri is an emeritus professor in the University of Notre Dame's Department of Chemistry and Biochemistry. He graduated from Northern Illinois University with a BSc in Chemistry and Mathematics and a PhD in Physical Analytical Chemistry from the University of Utah.


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