How to formalize this paradox?

Question

A friend gave me this problem (in the "blue box")

An interesting fact about the number $2$.

How many times the number $2$ appears in this text?

It appears $2$ times.

Well I see the number two $3$ times but if i put $3$ in "It appears ... times." it becomes false ...

$(1)$How we can rewrite this paradox in the classical logic (cutting useless parts, can this paradox be reduced to a simple form?)?

$(2)$What is its deep meaning and where comes from?

The weird thing I notice, that maybe is the cause, is that the 3rd phrase try to state something about itslef and the system..even if it is inside the system...

My intepretation

My attempt to find a similar "paradox" inside naive sets theory's concept is :

lets define two sets $A=\{2\}$ and $B=\{\delta \}$ , $2$ and $\delta$ are finite ordinals

then lets define a set $X=A\cup B$

We have that $|A|=|B|=1$ and we know that $|X|=|A|+ |B|-|A\cap B|$

now we say that $|X|=\delta$ that can be

$\delta=1$ (if $A\cap B=\{2\}$ ) or

$\delta=2$ (if $A\cap B=\varnothing $ )

then $|A\cup B|=\delta=1 \rightarrow A\cap B=\{2\}$

but $A\cap B=\{2\} \rightarrow ((2\in A) \land (2\in B)) $ and we know that in $B$ ther is only one element so $2=\delta$

If this "paradox" is of the same kind of the first (inside the "blue" box) now I can see better that there is something circular. Anyways I'm not able to continue and find a simple (and correct) formula in the language of classical logic that shows this problem, so my questions $(1)$ and $(2)$ are still valid for me.

UPDATE

As the user Charles noticed my interpretation I can't redefine define the two objects.

In fact I wanted to obtain the paradox with that:

$i)$ $ A:=\{2\}$

$ii)$ $B=\{|X|\}$

$iii)$ $X = A \cup B$

these tree definition aren't ordered, are given at the same moment, but the definiton is circular because I use $ii)$ in $iii)$ and viceversa.It is maybe this the origin of the paradox?

But what I am really interested in is:

$1)'$ Can be my friend's text reduced at this? How can I express this with a formal formula? (Like the Russel's paradox for example)

that is the question 1).

Answer 1

An interesting fact about the number 2:
How many times does the number 2 appears in this text?
It appears 2+1 times.

Answer 2

This is an attempt to answer the new question.

I don't think this is a paradox. You've already defined $X$ and $\delta$ so it's not legitimate to redefine them with

now we say that $|X|=\delta$ that can be

If this is instead treated as a condition

For what $\delta$ does $|X|=\delta$?

then the answer is simple: there are no such $\delta.$