Q.Write a program to swap two numbers without using a third variable.

Variable Assignment Order — First Principles

Imagine you are following a recipe. The recipe says: "Take the number of eggs, call it $x$. Then take $x$, add 2, and call the result $y$." You would never dream of using $y$ before you have defined $x$ — that would be nonsense. Variable assignment order is simply the rule that a variable must be given a value before it can be used in any expression that defines another variable.

The Intuition

Think of a variable as a labelled box. You cannot take something out of a box that is empty. When you write:

$x = 5$

$y = x + 3$

you first put the number 5 into box $x$, then you look into box $x$, take out the 5, add 3, and put the result (8) into box $y$. The order is: define first, use second.

Now consider what happens if you reverse the order:

$y = x + 3$

$x = 5$

At the moment you try to compute $y$, box $x$ is empty. The expression $x + 3$ has no meaning — it is like asking "what is nothing plus 3?" In most programming languages and in mathematical reasoning, this is an error. The variable $x$ has not yet been assigned. …