Warp wrote:
>   Some relatively easy math problems for your consideration and enjoyment:
> 
> 
>   1)

Key phrase: "not divisible by any *of the* primes"


>   2) 

Some of the permutations will be repeat the same sequence.


>   3) 

This value is bounded below by:

	(1/4) * sum_{i=1:inf} 1/sqrt(i)

Which diverges, so the expected length of the game is infinite.


>   4) 

I don't see how this is possible to give in closed form unless you allow 
the ability to sum the digits in the base-5 representation of a number 
(which you'd need a recursion or summation to do).  If you actually know 
a closed form that doesn't use a cheat like this I'd be curious to hear it.

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