# Differs

# Differs

**Differs** is an English locksmithing term that refers to the number of possible keys for a given lock. This number is a factor of the design of the key, the number of locking components, the number of available positions for each component, and the tolerances of the lock. Tryout keys are a lockpicking tool used to exploit a low differ count in certain locks.

In keyless combination locks, the number of differs may be referred to as permutations, combinations, or sequences.

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## Real vs. Theoretical Differs

Differs are divided between theoretical and real. Theoretically, most locks have a very high number of differs but in reality tolerances and bitting restrictions lower this number dramatically. For example, a 5 pin lock with 10 depth spacings has 10^{5} (100,000) theoretical key differs. Various key or lock requirements may lower this number dramatically:

- Cut depths cannot be repeated more than twice in a row.
- Cut depths changes cannot be greater than a certain number. This is usually done to prevent back-cutting during key removal. (See MACS)
- Cut depths cannot follow predictable or easy to pick patterns, such as a staircase.
- Tolerances of the lock allow for fractional depths to correctly set components.
- Certain types of master keying may restrict various cut depths in non-master keys.

In rotary combination locks, the size of gates has a dramatic effect on the number of possible permutations. Poor quality locks may have tolerances as low as +/- 3 numbers. In addition, most rotary combination locks have an area of the wheel that cannot be used for the last part of the combination, sometimes referred to as the restricted zone or the danger zone.

## Calculating differs

Differs in a standard lock design are calculated with the formula a^{b}, where a is the number of variations per component and b is the number of components. For example, a pin-tumbler lock with 5 pins and 8 depths per component has 32,768 (8^{5}) theoretical differs.

The number of differs in a lock with multiple sets of components is the product of all component groups combined. For example, the same 5 pin lock with 8 depths may also have a 5 pin sidebar which allows 4 depths per sidebar pin. The total number of differs for this lock would be 33,554,432 (8^{5}*4^{5}).

### Including MACS restrictions

In locks that have a defined MACS the number of real key differs is reduced. For example, in a system with a MACS of 5, a 1 and 8 pin could not be placed next to each other. Calculating the number of real differs for a MACS system requires finding all theoretical differs then discarding all permutations that violate the MACS.

## Calculating permutations

Permutations can also be calculated for keyless combination locks. The number of theoretical permutations is a^{b}, where a is the number of wheels and b is the number of dial graduations. I.e., a three wheel, 100 number combination lock would have 1,000,000 (100^{3}) theoretical permutations. The manufacturing tolerances of all mechanical combination locks lowers this number, some to an extreme degree.