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If anyone needs any help with the PoW, I will probably be on AIM until around 10 tonight, but I may not be able to help that much. Spedlyf is my AIM.

Thanks for offering to help folks, Peter. We did do a fair amount of work on the POW in class on Friday. I'm going to try to summarize some of what we did.

First, I posted a table of values for the number of moves needed. In this table a_{n} stands for the number of moves needed with n switches:

Next, I gave the hint that there are two rules for this table - one for when n is odd and a different one for when n is even.

We noticed that you can state these rules as:

When n is odd a_{n+1 }= 2a_{n}

When n is even a_{n+1} = 2a_{n}+1

I mentioned that these are recursive rules and what you are really looking for are non-recursive rules that will tell you a_{n} just as a function of n, without having to know any previous value.

The final hint I gave was the these non-recursive rules can be written as:

First, I posted a table of values for the number of moves needed. In this table a

n |
a_{n} |

1 |
1 |

2 |
2 |

3 |
5 |

4 |
10 |

5 |
21 |

6 |
42 |

7 |
85 |

8 |
170 |

Next, I gave the hint that there are two rules for this table - one for when n is odd and a different one for when n is even.

We noticed that you can state these rules as:

When n is odd a

When n is even a

I mentioned that these are recursive rules and what you are really looking for are non-recursive rules that will tell you a

The final hint I gave was the these non-recursive rules can be written as: