Brain Puzzler For Today..

Imagine a bacteria which, when having access to a source of food, will double in number every minute. So starting with one, we have two, one minute later, then four a minute after that etc. etc. for as long as there is food available.

Now imagine that scientist bloke off the Muppets puts just a single cell of this bateria (or a single bacterium) into a bottle, with plenty of food, and leave the room. It is 8.00am. When they (he comes back with that annoying Beaker thing) return at 12.00pm, ie. four hours later, they arrive just in time to see the very last scrap of food being devoured, and the bottle being completely saturated, ie. full of bacteria.

Now the question - at what point in time did the bottle become a quarter full?...


....think about it....




.....this can actually be done to the nearest minute...




....if you can't get the solution or can't be arsed, scroll down a bit..




...the time the bottle became a quarter full was 11.58 a.m., ie. only two minutes before the scientists returned!

Well done if you got it, if not, you probably stumbled on the fact that you tried to calculate the answer going from the beginning, with 1, 2, 4, 8, 16...bacteria....and of course it's impossible to say how many bacteria constitute a quarter-full bottle anyway.

The key is to start from the end. If the bottle becomes full at 12.00pm, that means one minute before, at 11.59, it's half full (since the number doubles every minute), and thus a minute before that, it's a quarter full. Therefore, a mere seven minutes before the finish, or 11.53am, the bottle is only 1/128th, or less than one per cent, full.

This has a wider application in fact, and I originally heard about it in the context of pyramid selling, where newcomers were being duped into parting with a lot of money in order to 'get started' in a market that seemed to have had very limited penetration, thus providing very fertile ground for making a lot of sales in comparison with other, more saturated markets. In reality, the market was at 11.53 a.m. or thereabouts, as if by magic it suddenly became quarter, then a half, then completely full, and the hapless would-be salesperson was left scuppered.

On the other hand the mould in the cup I left in the cupboard under the sink seems to be multiplying at an even more rapid rate..