04 Oct '10 20:23

"If you've done six impossible things this morning, why not round if off with breakfast at Millyways?"- Douglas Adams

Suppose you and your friend come into possession of a bag of infinite capacity, along with an infinite supply of numbered balls and a stopwatch with an infinite number of gradations. After watching the universe explode over mimosas and eggs Benedict at the Restaurant at the End of the Universe, the two of you decide to pass the time by running the following experiment:

1. You begin by placing two balls (balls 1 and 2) into the bag, then set the stopwatch to count down from 60 seconds.

2. When the stopwatch reads 30 seconds, you place two more balls (balls 3 and 4) into the bag and your friend pulls out the first ball you placed in the bag (ball 1).

3. When the stopwatch reads 15 seconds, you place two more balls (balls 5 and 6) into the bag and your friend pulls out the second ball you placed in the bag (ball 2).

4. The two of you repeat this process, you placing the next two balls into the bag and your friend removing the oldest ball, each time the remaining time on the stopwatch is halved (i.e. 7.5 seconds, 3.75 seconds, 1.825 seconds, etc...).

**Question:**How many balls will be left in the bag when the stopwatch reads 0 seconds?