76 replies to this topic

[rookie1ja]

Virile Microbes - Back to the Logic Puzzles
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?

This old topic is locked since it was answered many times. You can check solution in the Spoiler below.
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Spoiler for Solution

Biology - solution
The dish will be full at 12:44.

Answer for old wording:
The saucer was half full at 11.59 - the next minute there will be twice as many of them there (so full at 12.00).

Spoiler for old wording

Let's say some primitive organisms divide themselves every minute in two equal parts that are the same size as the original organism, and which also divide the next minute and so on [wording amended]. The saucer in which we started observing this process was full at 12.00.
When was it half full?

[gloohead]

Actually - when a cell divides each cell starts out 1/2 as big. So even though the number doubles every minute - the same CAN'T be said about the size. So if the plate was full at 12:00, it was pretty much full at 11:59. Growth and division are not the same thing.

[rookie1ja]

That's right. And that's why I clearly stated in the puzzle that:

Let's say some primitive organisms divide themselves every minute in two equal parts ...

So I made the condition that their sizes are equal.

[aman2big]

So I made the condition that their sizes are equal

sorry I could'nt let this one go, but

divide themselves every minute in two equal parts

doesn’t make the condition that their sizes are equal true...you can cut a slice of toast in two equal parts and it doesn’t mean you have two slices of toast the same size as the original before you divided.
the question wasn't explained clear enough and should be edited.

[rookie1ja]

You are right - I read the puzzle too fast. I changed it accordingly.

[Skumbag]

Actually - when a cell divides each cell starts out 1/2 as big. So even though the number doubles every minute - the same CAN'T be said about the size. So if the plate was full at 12:00, it was pretty much full at 11:59. Growth and division are not the same thing.

?
That means that the total size of all the resultant cells (no matter how many there were) would forever equal the size of the original cell! Babies aren't born microscopically small, you know.

That is not a case of a cell dividing, it's a case of a cell slowly falling apart!

[fosley]

I think this is what Gloohead was saying:

Time......Cell Count.......Area Covered (assume vertical thickness doesn't change)
11:58.....500...............10.0 cm?
11:59.....1000..............10.1 cm?
12:00.....2000..............10.2 cm?

Basically, the number of cells keeps doubling every minute, but the individual cells don't grow from tiny to big every minute.

Of course, I would tend towards thinking the cells wouldn't divide until they'd reached a certain size, so if they were doubling in number every minute, they'd probably also double in size every minute. (And consuming twice as much food every minute. . .)

[lovinitmtboy]

I am going to have to disagree with the answer, because the saucer could have potentialy been "full" at 11:00, or even 10:00, If it is full, the resulting divisions are no longer contained. So the answer is not known. Unless I totally missed something.

[larryhl]

the question isn't worded very well. it still says "Let's say some primitive organisms divide themselves every minute in two equal parts which also divide the next minute and so on." 2 equal parts doesn't mean the same size as original organism.

a better wording would be "Let's say some primitive organisms divide themselves every minute in two equal parts that are the same size as the original organism, and which also divide the next minute and so on."

[mynameisjjonas]

I have to agree with lovinitmtboy. There was no basic limit on the start time. So, let's assume it was started the previous day at noon. It would definitely be full at noon the day it was checked.
I still think this was a good logic puzzle, just vague.