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.
Show that for any number a, there is a number x such that x gives ax.
It's about strings really.
The effect of the two instructions is:
If a nunber string begins with '21', then crop the first two digits and duplicate the rest ('y' and 'y')
String '21a' therefore gives 'a' and 'a'.
So for any number a, x = 21a21 gives 'a' and '21a21' = a and x
Posted by broll
on 2014-12-04 01:26:07