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# Biology

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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?

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Biology - solution

The dish will be full at 12:44.

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).

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?

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• 3 weeks later...
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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.

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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.

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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

doesnâ€™t make the condition that their sizes are equal true...you can cut a slice of toast in two equal parts and it doesnâ€™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.

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

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• 3 weeks later...
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!

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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. . .)

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• 3 weeks later...

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.

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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."

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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.

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you guys over complicate the puzzle. it is as simple as 11:59 like he said. u guys act just like the kids at the spelling bee when u get a simple question it seems too easy u have to screw it up with over complicated theories

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• 2 weeks later...
? 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.
Ok: when cells divide at first, they are half the size of the original cell. Then in the G1 stage of interphase, they start growing. So eventually they would double in size. But just before cell division, cells appear to be "bloated" anyways, so the new cells would be half the size of the original, but not necessarily half of an average cell.

But for the purposes of this puzzle, they would be equal in size after each division. And also, we have to assume that the saucer's space was used up at 12:00, otherwise we wouldn't have an answer. But under normal circumstances, we wouldn't know when it turned full, because division would stop as soon as the space was used up.

11.59

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wow, you guys need to chill out.

-'cell division' the only condition was that it was a primitive organism. nothing was said to indicate that it was even cells dividing so all your knowledge about cell division is useless.

-'equal parts', what the frick did you think it meant? equal as in equal rights? equal as in equal color? please

-'the pitre dish would've been full' depends on how big the pitre dish was (see how stupid questioning that assumption sounds, well that's how stupid you sound when you split hairs with this puzzle), and even if the divisions started a year ago, if they were infinitesimally small enough (and even if they weren't) the fact still remains that at 11:59 the dish was half full and therefore at 12:00 it was completely full

don't be a baby just because you didn't get it right

-and yes, i do mean to sound like a jerk because you need to get a life and stop being a baby when you can't figure something out based on assumptions a 3 year old would make

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-'cell division' the only condition was that it was a primitive organism. nothing was said to indicate that it was even cells dividing so all your knowledge about cell division is useless.

-'equal parts', what the frick did you think it meant? equal as in equal rights? equal as in equal color? please

-'the pitre dish would've been full' depends on how big the pitre dish was (see how stupid questioning that assumption sounds, well that's how stupid you sound when you split hairs with this puzzle), and even if the divisions started a year ago, if they were infinitesimally small enough (and even if they weren't) the fact still remains that at 11:59 the dish was half full and therefore at 12:00 it was completely full

don't be a baby just because you didn't get it right

-and yes, i do mean to sound like a jerk because you need to get a life and stop being a baby when you can't figure something out based on assumptions a 3 year old would make

Ok, you should stop assuming that I couldn't figure it out. I did. I was clearing up several irregularities that other readers have pointed out.

[*]The word organism implies that it is made of cells, and cells divide by mitosis (a form of cell division), so yes, cell division applies. But since the question states that each generation of cells is the same size, then cell division doesn't matter. As I said, I was only clearing up the subject of cell division.[/*:m:e1c89]

[*]Yes, I agree with you on this point. It should be automatically assumed that the problem means that each generation is the same size. But in truth the problem didn't quite stipulate that the same size carried into all subsequent generations when it was first posted, so several other readers who were expecting something more in the problem thought it meant something other than what was intended.[/*:m:e1c89]

[*]Yes, that is true only if the dish only became full at exactly 12:00. Say for example that the dish was half-full at 9:59. Then it would be completely full at 10:00. There is no more room for division, so mitosis stops. The dish is still full at 12:00. It fills the conditions, however, this is overcomplicating the problem, and while I don't like assuming in problems like these, you just have to assume that it only turned full at 12:00, which gives you the answer of 11:59.[/*:m:e1c89]

~

~

Numenor

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i'm not sure how many of your arguments i attacked but i wasn't trying to single anyone out. i agree with all of your rebuttals to my rebuttals. anonymity in online forums is a weakness for flaming for me i guess. i hope i didn't upset you too much, if at all. like i said, i knew i was being a jerk, hopefully that quelled the rage a bit. anywho

1. i agree, biology has never been a strong subject for me and i didn't bother looking up the technical definition of 'organism'

3. i guess i didn't understand that way of looking at it

sorry again

cheers

11:59

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Some facts for the realists (as opposed to the logical theorists):

- Cells get slightly bigger before they divide so the two new cells are big enough to sustain themselves (no infinitely small cell divisions)

- Cells must consume food in order to grow large enough to reproduce (split)

- It is sufficient to assume that the cells in this puzzle consume enough food and grow large enough to split within 1 minute

The most significant problem this causes with the solution:

There has to be enough food in the saucer to allow the cells to completely fill it after dividing, eating, repeat.

If we postulate that absolutely no waste material is discarded, then the total food requirements are a full saucer's worth.

Thus, the experiment started at 12. ;-)

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Ok, guys this is supposed to be a fun riddle. If, you don't like it this way then how about this? There is a jar with 2 flies in it, every minute the number of flies doubles. So, at 1 minute there are 4 flies, at 2 minutes there are 8 and so on. If the jar is completely full with 400 flies at noon, what time was the jar half full? Is that better? Or, are you bio nerds going to attack this riddle too?

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for that the first thing is we should know the size of the saucer.

we dont know how big it is???.

if i assume its area as 10cm^2

other person may assume something else.

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Is that better? Or, are you bio nerds going to attack this riddle too?

Well, I'm not a bio nerd, but your riddle is exactly the same as the previous one. Flies gotta eat to reproduce.

Big Tony has loaned you 1 penny at 100% interest, compounded minutely (time, not size).

When the amount you have to pay back exceeds your yearly pre-tax salary (you make 100,000 \$/year), he will come in to break your legs.

A few seconds after 12:00:00, he came in with a baseball bat and 3 goons. When did he loan you the penny?

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WHOOPS! A couple of big mistakes.

1) My riddle is for a completely different solution. I'm asking for the start time, not the "half full" time.

2) The original riddle is fatally flawed. Even if we accept the intended "magical reproduction at same size, each minute" rule as a given, we still don't know when the saucer gets half full!

The reason being that we don't know the size of the cells nor the size of the saucer, both of which are absolutely essential to answering this question. For example:

Suppose the saucer can hold exactly 10 cells.

After 1 minute, the saucer has 2 cells, but is not half full.

After 2 minutes, 4 cells, but is not half full.

After 3 minutes, 8 cells, more than half but not completely full.

After 4 minutes, completely full.

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I think it would be half-full at 11:59, because then at the next minute (12:00) assuming that 12:00 isn't minute and seconds, but noon or midnight since when half is doubled it makes a whole. If in fact it's not hours and minutes, but minutes and seconds (like on a stop watch), the correct answer would then be 11:00.

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11:59 Within the contraints of the riddle, the organisms double in number every minute. At 11:59 it was half-full, doubled in size and the saucer was completely full at 12:00.

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11:59 Within the contraints of the riddle, the organisms double in number every minute. At 11:59 it was half-full, doubled in size and the saucer was completely full at 12:00.

Unless it went from 40% full to 80% full with no stop at 50% full.

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This topic is now closed to further replies.