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?
...2121.
Since 121 gives 21,2121 gives 2121.
We can find an i such that for any number x,ix gives xx,so ii will give itself.
21x gives xx since 1x gives x,and so 21 is an i.
2121 must give itself.
Good problem,Tim.
It is...
