Question 196060
Let X be the number you choose. X can be anything except 1.

Following the instructions:
Square it
{{{X*X}}}
Subtract 1
{{{(X*X) -1 }}}
Divide by 1 less than the original number (Now you know why the original number can't be 1)
{{{((X*X)-1) / (X-1)}}}
Now subtract the original number
{{{(((X*X)-1) / (X-1) - X)}}}

Now get things over a common denominator
{{{(((X*X)-1) - (X-1)*X)/(X-1))}}}
Expand
{{{(X^2 - 1 - X^2 + X)/(X-1)}}}
Simply
{{{(X-1)/(X-1)}}}
{{{1}}}

So that's how that one works.

You can do that same type of idea to make up your own problem.
Here's one
Pick a number between 0 and 49
Add 50
Multiply by 2
Subtract your original number
Subtract 100
What do you get? Ans: Original number
Why?