On Wed, 04 Dec 2013 06:54:53 +0000, Dave Baker wrote:

I also started
off by ticking 3/4 for the lemonade question as that initially seemed
intuitively right but took care to scribble the descending series on an
envelope and sum the fractions before pressing enter and was quite
surprised to find it was actually 2/3. A little more thought then
revealed that the second person to drink must consume more than half of
the half pint that he starts with and so the first person could never
reach 3/4. Hey ho. So much for initial intuition.

You don't have to sum the series: each time round the first person gets
twice what the second gets so ends up with 2/3 the whole

--
John Stumbles

I forgot to take my amnesia medicine again

John Stumbles put finger to keyboard:

On Wed, 04 Dec 2013 06:54:53 +0000, Dave Baker wrote:

I also started
off by ticking 3/4 for the lemonade question as that initially seemed
intuitively right but took care to scribble the descending series on an
envelope and sum the fractions before pressing enter and was quite
surprised to find it was actually 2/3. A little more thought then
revealed that the second person to drink must consume more than half of
the half pint that he starts with and so the first person could never
reach 3/4. Hey ho. So much for initial intuition.

You don't have to sum the series: each time round the first person gets
twice what the second gets so ends up with 2/3 the whole

Reminds me of the old joke:

An infinite number of mathematicians go into a bar.

"Pint of beer, please", says the first.
"Half a pint, please", says the second.
"Quarter of a pint please", says the third.
"One eighth of a pint, please", says the fourth...

"You're all idiots", says the barman, pouring two pints.