I have a number machine.
I say x gives y if when x goes in, y comes out.
For any numbers x and y, by "xy" I mean x followed by y.
Here are my two rules.

1x gives x.

For example, 13 gives 3.

If x gives y, then 2x gives yy.

For example, 213 gives 33 since 13 gives 3.

What is a number that gives itself?

Why is this in algorithms? I thought this category was for problems which require computer programs to solve?