On 04/12/2013 12:42, Bert Coules wrote:
Thanks for that: fascinating. I'm obviously missing something
fundamental in the milk-drinking question: at first glance the amounts
drunk would seem to be 1/2 + 1/4 + 1/8 + 1/16 and so on, but unless my
maths is even worse than I think (which is entirely possible) I can't
make that add up to 2/3.

That series should add up to 1.

Can someone explain in numbers of one syllable please?

If you think of it as a two player game.

Whatever A drinks then B drinks half as much on his turn.

A drinks 1/2 + 1/8 + 1/32 + 1/128 + ...
B drinks 1/2(1/2 + 1/8 + 1/32 + 1/128 + ...

The whole is therefore divided into three & A gets 2 parts.

Variants can then include each player drinks 2/3 of the remaining liquid
which is a bit harder to get right. It was beer in my day.

--
Regards,
Martin Brown

Thanks for all the replies. Stupid of me: I was shooting past the
requirement to drink only half of what remains each time.