## Damn you, maths

A Petri dish hosts a healthy colony of bacteria. Once a minute every bacterium divides into two. The colony was founded by a single cell at noon. At exactly 12:43 (43 minutes later) the Petri dish was half full.

At what time will the dish be full?

February 6th, 2013 at 7:23 pm

Let me guess, you said 12:44?

February 6th, 2013 at 8:05 pm

I got this one even without a fancy Ivy League edumahcation.

February 7th, 2013 at 9:46 am

Alceste, no i did not. what’s your answer?

February 7th, 2013 at 1:47 pm

The actual answer is 12:44. Half full, then, doubles to full the next minute.

February 7th, 2013 at 2:40 pm

As question is written, my answer is never. There’s no reason (from this particular phrasing of the question) to assume that each generation of bacteria is the same size as the prior generation. The bacteria are not doubling, but instead dividing into 2. So the area/volume of the set of all bacteria remains constant as each successive generation of bacteria gets smaller at the time it’s split. Of course, the bacteria could grow after it splits (and maybe it’s the case that the cells split every time they reach a certain size equal to the original size), but there’s no way to know the rate of growth of an individual cell from the way the question is worded.

(On the math, assume the petri dish is rectangular 2″x1″x1″ — 2 cubic inches. I place a 1″x”1″x1″ cube in the dish. That’s 1 cubic inch. We can say dish is now half-full. If I divide the cube into two down the middle, I now have two rectangular solids that are 1/2″x1″x1″ — or 1/2 cubic inch each. Total volume of the two new solids is 1 cubic inch, so we’re still half-full. You can keep doing that until each subdivision gets infinitesimally small, but the total volume of the subdivisions will still be 1 cubic inch.)

February 7th, 2013 at 2:45 pm

I hate you. So very much.

February 7th, 2013 at 8:31 pm

So what was your answer? (And why?)

February 7th, 2013 at 8:33 pm

And why do you keep finding yourself drawn to poorly worded logic puzzles?

February 7th, 2013 at 9:29 pm

Are these puzzles for children?

February 7th, 2013 at 9:31 pm

I like this one –

You drive up a mountain that is 10 miles up and 10 miles down, and averaged 30mph for the first 10 miles. How fast would you need to go to for the remaining 6 miles to average 60mph for the entire trip?

February 8th, 2013 at 10:07 am

I think you messed up the wording of your puzzle.

February 8th, 2013 at 10:07 am

@Alceste Don’t ask. Suffice to say I overthought it. And not in a good way. #WOMP

February 8th, 2013 at 4:27 pm

Yes, i did – should read –

You drive up a mountain that is 10 miles up and 10 miles down, and averaged 30mph for the first 10 miles. How fast would you need to go to for the remaining 10 miles to average 60mph for the entire trip?

February 8th, 2013 at 5:43 pm

I can’t find the “impossible” key on my phone. #womp