Assuming you couldn't ask anyone else their number, th best guess would be your own number.
There is a set of twenty numbers to consider, one each of 0 through 9, and one digit that is the 100 factorial'th digit of Pi, which is calculable, repeated ten times. Anyways, thus the 100!-th digit of Pi is represented in the set of 20 numbered denizens of the universe 11 times. It is more than %50 likely, %55 likely, that the number one receives is the number in question. It is a simple probability. Reference Vegas.
Wei Dai wrote:
> Suppose you wake up in a universe which contains a total of 20 people. Ten
> of them have been assigned numbers 0 to 9, and the other ten have been
> assigned the number equal to the 100!-th digit in the decimal expansion of
> PI. You are told your number but not anyone else's, and you are
> asked to guess the 100!-th digit of PI. Assuming that you can't actually
> compute that digit, it seems intuitive that your best guess would be your
> own number.
> My questions are (1) is this correct and (2) are there principles of
> reasoning under computational limitations (perhaps extensions of
> probability theory?) that can be used to derive or justify this and
> similar conclusions? Any relevant references would be appreciated.
-- Ross Andrew Finlayson 202/387-8208 http://www.tomco.net/~raf/ "C is the speed of light."