I was reading the io9 article Why four is the nemesis of happy numbers and it got me thinking. Are there actually any cycles other than the one stated in the article? Why or why not?

I was reading the io9 article Why four is the nemesis of happy numbers and it got me thinking. Are there actually any cycles other than the one stated in the article? Why or why not?

Lifehacker had an interesting post today where they outlined a simple dice game where you have three distinct six-sided dice, each with a different number scheme. The neat thing was that the dice had a mutually intransitive set of win probabilities, similar to rock paper scissors. So if your opponent chooses first and you choose the die that has the 5/9 edge over theirs, you will win about 5% more of the rolls (1/18).