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Cheers for this, I didn't know the mathematical basis for it, but our eldest child brought this "puzzle" home for year 7 homework a while ago. We spent the weekend experimenting with loads of bits of paper on the floor coming to the conclusion that once you land on a base 2 number, you have a path directly back to 1.

He learned binary in a weekend and we had a fun few days hacking math :)

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Don't you mean on an even number? Or just a power of 2? Or are you talking about a base 10 number that's composed of all 1's and 0's? (All natural numbers are base 2 numbers...)

Also related: http://xkcd.com/710/

Sorry, I mean a power of 2 :)

It's very interesting to watch in binary, actually.

You first check if the LSB is 1. If not, you right shift it until it is. Once the LSB is 1, you add it to itself shifted left by one bit, then increment.

Watching the bits go by and shrink over time reminds me of cellular automata in a way.

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