Variation lock seems more accurate by mathematical definitions

Edit(to give it more context)

  • Hey, can you tell me the combination of your lockbox ?

Why don't we say variation(or permutation)? The order matters in this case and combination is an unordered set of numbers.


6 Answers 6


Because most people are not mathematicians.

I know that sounds like a flippant answer, but it's genuinely the answer. There are many words which have a more precise (or even different) meaning for specialists, and the fact is that these words simply have both meanings. The question "Is a tomato a fruit or a vegetable?" is an all too familiar example: to a botanist, it's a fruit; to most of us, it's a vegetable.

So the fact that mathematicians use "combination" in a more restricted way is irrelevant to almost everybody who uses the locks.

  • 14
    Knowledge is an awareness that tomatoes are fruits. Wisdom is an awareness that tomatoes don't go in a fruit salad.
    – rob
    Dec 21, 2018 at 5:40
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    Correct and upvoted but for me the main point is that mathematicians took an English word and gave it a special meaning. Similarly, the words "real", "natural", and "rational" have special meanings in mathematics. These words were all pre-existing and were borrowed and given new meanings intentionally. Of course, it still bugs me that people refer to musical "groups" when none of them have an an associative binary operator. Dec 21, 2018 at 13:05
  • And is ketchup a smoothie?
    – Lenne
    Dec 21, 2018 at 20:29
  • @HughMeyers: I remember John Conway giving a talk (in recreational maths) where he described something (can't remember what) as "reducible", abbreviated it to "red", and henceforward wrote it in red pen. He appealed to the audience for a similarly snappy way of referring to "irreducible" whatevers.
    – Colin Fine
    Jan 3, 2019 at 14:39

combination is an unordered set of numbers

That is incorrect in general English.

It is called a combination lock because (in general English)
a combination is "an ordered sequence" (Merriam-Webster definition 2a).

You tagged the question with: , , and , but you won't get an answer that combines the three because mathematics/statistics give the term "combination" a specific meaning which is (usually) at odds with the general English use case.

It is however, common enough to be in the dictionary definition referenced above (definition 2c).


COMBINATION means an arrangement in a particular order that can be used to open some types of lock. Combinations can be hideous or horrible or agreeable.In combination lock we imagine that agreeable situation that unlocks. 'Variations' does not give this idea of agreement of one with the other. An example:

  • She had then shot the bolts and turned the knob of the combination as she had seen Mr Adams do.(Jimmy Valentine — by O. Henry)

Examples have been found from Roman times and museums have examples circa 1200 when, the Muslim engineer Al-Jazari documented a combination lock.

enter image description here enter image description here

CC-BY-SA 3.0 Sigismund von Dobschütz

Perhaps the name was popularised since 1909 because it was patented as a physical object, not a mathematical concept.

Thus it's the way that "word combination" locks the usage.

My invention is an improvement in locks and consists in certain novel constructions and combinations of parts hereinafter described and claimed.

enter image description here

The object of the invention is to provide a combination padlock, of simple and cheap construction, which will be strong and durable, and not liable to get out of order easily, and in which the combination may be easily changed.

Origin of combination 1350–1400; Middle English combinacyoun (
Middle French ) < Late Latin combīnātiōn- (stem of combīnātiō )

It is simply the combination of characters that let us pick holes in the term.


Because it is a combination of different dial positions. Since the dials themselves are in a fixed order, this combination automatically implies a permutation. e.g. Create a combinition, by picking one (out of ten) ball each from k bins. Now given a fixed order of bins, a permutation already gets decided when the combinition is created. See the point


Many cheap combination locks are in-fact combination locks and not permutation locks. For some the order does matter, but for others the order does not matter. Both are called combination locks in English. It makes sense that we use one term to describe both.

I'm not certain of the etymology but it's possible the original design required a combination and the increase in security to require a permutation was a later development. In which case it was originally a mathematically accurate term, but became less so when both types were available. Either that or the word was never used here for its precise mathematical definition.

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    I've never heard of a combination lock where order doesn't matter. Do you have any examples of those? Dec 20, 2018 at 13:55
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    The mechanical push-button locks on doors are often order-insensitive
    – CSM
    Dec 20, 2018 at 15:40
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    @TannerSwett I believe this is an example: gamut.com/p/surface-mount-key-lock-box-NjY3NDMz The number of combinations listed is 1000. If each number from 0 to 9 can be either included or not, that gives 2^10 = 1024 possibilities, which seems to have been rounded to 1000. Dec 20, 2018 at 16:56
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    Yes the example I was thinking of was door button locks. Dec 20, 2018 at 22:08
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    @Acccumulation: I question your math. "Combination" locks traditionally require the entry of three numbers. If the key lock box that you found and linked to requires three button presses, where order matters (and buttons can be used more than once), then the number of possible combinations is 10^3, which, of course, is exactly 1000. Dec 23, 2018 at 5:43

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