When to use this
Use this formula when the question matches this rule set
Use this for three-position locker-style numbers, puzzle dials, or any 3-slot code where each position can reuse any allowed value.
What this result means
Interpret the output, not just the number
The result counts every ordered code the lock can display. 05-12-59 is different from 59-12-05, so order matters. Reusing the same value on more than one dial is allowed, e.g. 00-00-00, so the formula is n^r.
Formula: n^r
Calculator inputs
Know what to enter in each field
These pages use lock language, but the math is permutation with repetition: order matters, repeats are allowed, and the count is n^r.
Number of dials / positions
This is how many ordered slots the code uses.
What to enter: On the dedicated lock pages this value is preset by the page title.
How to use it: Each extra dial multiplies the total again because a code like 1234 is different from 4321.
Example: A three-dial lock uses 3 positions, and a four-dial lock uses 4.
Pool type
Choose whether each dial uses a generated range or a custom symbol list.
What to enter: Pick Range for numeric spans like 0-9 or 0-59, or Custom list for tokens like A,B,C,D.
How to use it: The calculator counts how many allowed symbols each dial can show, then raises that pool size to the number of positions.
Example: A lock labeled 0-59 uses Range. A puzzle lock with A,B,C,D uses Custom list.
Range start / range end
These define the first and last values available on every dial when using Range.
What to enter: Enter the full inclusive range used on each dial.
How to use it: The pool size is end - start + 1, so 0-9 gives 10 symbols and 0-59 gives 60 symbols.
Example: A three-number locker dial usually uses 0 through 59.
Custom symbol list
This defines the allowed symbols directly when the dials are not a simple numeric range.
What to enter: Enter comma-separated tokens such as A,B,C,D or 10,20,30,59.
How to use it: Each unique trimmed token becomes one available dial symbol. Duplicates and empty entries should be removed before solving.
Example: A letter lock using A,B,C,D,E has 5 possible symbols on each dial.
Worked examples
Quick checks with realistic inputs
Typical 0-59 lock
A three-number lock where each position can show any value from 0 through 59.
A 3-position lock code with 60 options per position has 216,000 possible codes.
Load this example into the calculatorCustom numeric symbol set
A three-dial puzzle lock where each dial is labeled 10, 20, 30, or 59.
A 3-position lock code with 4 options per position has 64 possible codes.
Load this example into the calculator