Does "Any of" mean "one of" or "all of"?

1. "Please use any of the five methods to solve the problem."
2. "Please use any of the methods to solve the problem."

Is there a difference between sentence 1 and 2?

I would think both sentences mean I only need to use one of the five methods to solve the problem. Is it correct?

Solution 1:

'Any one of the methods' would mean 'one method only'. Both 'any of the five methods' and 'any of the methods' mean 'one or more of the methods, up to and including all of them'.

Any refers to one, several or all of a total number.

Any (Cambridge Dictionary)

Solution 2:

The only difference between the two sentences in the question is that in the first sentence there are exactly five methods, whereas in the second sentence there is an indefinite number of methods.

As for the greater question:

？ Please use any of the methods to solve the problem.

The following do not mean the same thing:

✘ Please use one of the methods to solve the problem.
✘ Please use all of the methods to solve the problem.

One means exactly one, and all means exactly the number that there are.

But any is unspecified.

From Merriam-Webster's definition of any:

2 : one, some, or all indiscriminately of whatever quantity.

Given a total of 10 objects, any might result in just 1 object or all 10 objects being selected—but it could also result in a number between those two.

Any can also be also used to denote randomness rather than quantity.

For instance:

From these 10 items, select any 2.

In this sense, although the quantity is fixed, any is used to express the fact that your choice isn't limited to, for instance, the two items on the left; it doesn't matter which you choose.

Also from Merriam-Webster, this is a slightly different sense of any:

1 a : one or some indiscriminately of whatever kind : one or another taken at random
// Ask any man you meet.

If there is ambiguity in interpreting quantity versus choice, the sentence can be rephrased to be more precise.

For instance:

Please use any of the five methods to solve the problem.

This could be rephrased a few ways.

1. Please use only one of the five methods to solve the problem, but feel free to choose any of them.

Here, the quantity is fixed at one, but which method is available to be chosen is not limited.

2. Please use any of the five methods to solve the problem, and feel free to use as many methods as you like.

Here, both the quantity and choice are limited only by what exists.