> > Here's a math puzzle that's a lot easier to solve than it might seem at first. Can anyone do it?
> >
> > A number p is picked (by someone else) at random from a uniform distribution on the interval (0,1). Then a coin is crafted which, when tossed, results in heads with probability p and tails with probability 1-p. The coin is given to us without us being told what p is, and we have no way of deducing any additional information on the value of p besides experimentation.
> >
> > Given what we know, and since the problem's symmetric with respect to heads/tails, the chance of getting a heads is 1/2 on the first flip. I.e., we're 50% confident of getting heads when we're just about to make the first flip.
> >
> > The question is this: if we keep flipping the coin and getting heads, after which flip do we become 99% confident (or higher) that the next flip will also be heads?
>
> The trick I used was...

[eighty-four paragraphs about math snipped]

Uh... yeah. "A lot easier to solve than it might seem." Sure.

-Faux "You sort of lost me after 'The trick I used was...'" Pas.