why does “square one” not take an article?

Question

Consider the next idiom:

Go back to square one

For me, as a non-native speaker, putting the in front of square one sounds equally good as not putting it at all. But, when I speak with native speakers, for them saying the before square one sounds as a broken English.

On the other hand, if I take an another example:

There are a few problems. The first one is ...

My question is, what is the difference? Why in the case of idiom the should not be said, but in the second case it has to be said?

Answer 1

As a place name, 'square one' would not take an article.

Go back to square one.

I'm on square one of my journey.

However,

Go back to the square one.

...is perfectly fine depending on the context and inflection. By emphasizing 'square', you are saying go the square version of some thing, as opposed to the round one.

Your finger is on the round button, go back to the square one.

Answer 2

The image this idiom evokes is a board game with a sequence of 'squares' which players traverse. In the context of a sequence or ordered list we ordinarily refer to individual numbered items by Item + Number, with no article, because it is a unique identifier—in effect, a "name":

We will deal with this in more detail in Section 3.4.
Illustration 17 shows the so-called 'Chandos Portrait'.
Now look at Line 13 and track across to Column C—you'll see that the value has changed.
You have been bitten by an angry wombat and must return to base. Go back to Square One.

In the case of the first [problem] is you are not dealing with an ordered list but a random one: this is the problem you have elected to take up first.

Answer 3

If there is only one square, it is quite natural to say "the square". If there are a number of ordered squares, it is quite natural to say "square one", "square two", "square three" and so on. It would also be natural to say "the first square", "the second square", "the third square", and so forth.

The ordinal numbers (first, second, third) are ordinary adjectives. They don't count as determiners. When the series of squares is definite, "the first square" makes sense. When the series of squares is indefinite, "a first square" makes sense.

The cardinal numbers (one, two, three) behave a bit differently. When they appear after a singular noun that they modify, they do count as determiners. This usage only makes sense when the series is definite. Phrases like "square one", "chapter one" or "job one" don't need the definite article. The trailing number is definite enough.

Cardinal numbers can also appear as weak determiners before a noun. In this case (and with a single obvious exception) they modify plural nouns: "one square", "two squares", "three squares", etc. I call these determiners weak because they don't prevent the use of the definite article. "The one square" can still sound natural. "A one square", however, sounds completely wrong.

 
The structure of "the first one" is much like the structure of "the first square". Here, the "one" is a pronoun modified by the adjective "first". The series continues "the second one", "the third one" and so on.

The same structure exists when "square" is an adjective. In that case, "the square one", "the round one", "the thin one", "the tall one" and the like all sound perfectly natural. Those are simply ordinary adjectives modifying an ordinary pronoun.

In the phrase "square one", the "one" is a modifier, specifically a determiner. That's the same role that the definite or indefinite article can fill, so no article is required. In the phrase "the square one", "one" is a pronoun. "Square" is a modifier but it's not a determiner. The determiner role is filled by the definite article.

 
None of this has anything to do with the fact that "square one" is an idiom for "the beginning", or that it is almost always paired with the word "back".