Off Topic: A Math Puzzle

Hi Guys,
   My daughter is under the impression that I know 
something about mathematics.  In an e-mail she sent 
me the following puzzle:

  An amoeba is placed in an empty jar.  In one second 
  the amoeba splits into two amoebas, each as big as 
  the mother amoeba.  After another second the daughter 
  amoebas split in the same way.  As each new generation 
  splits, the number of amoebas and their total bulk 
  doubles each second.  In one hour the jar is full.  
  When is the jar half full?

I post this puzzle for your entertainment.

[-Rick-]

Den tirsdag den 30. september 2014 03.17.45 UTC+2 skrev Rick Lyons:
> Hi Guys,
> 
>    My daughter is under the impression that I know 
> 
> something about mathematics.  In an e-mail she sent 
> 
> me the following puzzle:
> 
> 
> 
>   An amoeba is placed in an empty jar.  In one second 
> 
>   the amoeba splits into two amoebas, each as big as 
> 
>   the mother amoeba.  After another second the daughter 
> 
>   amoebas split in the same way.  As each new generation 
> 
>   splits, the number of amoebas and their total bulk 
> 
>   doubles each second.  In one hour the jar is full.  
> 
>   When is the jar half full?
> 
> 
> 
> I post this puzzle for your entertainment.
> 
> 
> 
> [-Rick-]

one hour minus 1 second

-Lasse

On Mon, 29 Sep 2014 18:54:51 -0700 (PDT), langwadt@fonz.dk wrote:

>Den tirsdag den 30. september 2014 03.17.45 UTC+2 skrev Rick Lyons:
>> Hi Guys,
>> 
>>    My daughter is under the impression that I know 
>> something about mathematics.  In an e-mail she sent 
>> me the following puzzle:
>> 
>>   An amoeba is placed in an empty jar.  In one second 
>>   the amoeba splits into two amoebas, each as big as 
>>   the mother amoeba.  After another second the daughter 
>>   amoebas split in the same way.  As each new generation 
>>   splits, the number of amoebas and their total bulk 
>>   doubles each second.  In one hour the jar is full.  
>>   When is the jar half full?

>> I post this puzzle for your entertainment.
>>
>> [-Rick-]
>
>one hour minus 1 second
>
>-Lasse

Hi Lasse,
  Dog gone it.  You're too smart!!

I was hoping you'd do as I did--jump 
into the problem by writing a 
finite series equation and trying to 
solve the equation for a "half full jar."

Then after thinking about the puzzle
a little more carefully, it turns out 
to be super simple.

Good job Lasse.

[-Rick-]
I'll post a more difficult puzzle next time.

Rick Lyons <R.Lyons@_bogus_ieee.org> wrote:

(snip)
>   My daughter is under the impression that I know 
> something about mathematics.  In an e-mail she sent 
> me the following puzzle:
 
>  An amoeba is placed in an empty jar.  In one second 
>  the amoeba splits into two amoebas, each as big as 
>  the mother amoeba.  After another second the daughter 
>  amoebas split in the same way.  As each new generation 
>  splits, the number of amoebas and their total bulk 
>  doubles each second.  In one hour the jar is full.  
>  When is the jar half full?

Where is the jar?

There are about 2**265 atoms in the universe.

The volume of the universe in cubic fermis (fm**3) is about 1e136,
or 2**451.  (fm = 1e-15m)

After an hour, the jar has 2**3600 amoebae in it, so won't nearly
fit in the universe.

An unrelated question, which do you think has a bigger genome,
us or an amoeba?  

-- glen

On 9/29/2014 9:17 PM, Rick Lyons wrote:
>
>
>
> Hi Guys,
>     My daughter is under the impression that I know
> something about mathematics.  In an e-mail she sent
> me the following puzzle:
>
>    An amoeba is placed in an empty jar.  In one second
>    the amoeba splits into two amoebas, each as big as
>    the mother amoeba.  After another second the daughter
>    amoebas split in the same way.  As each new generation
>    splits, the number of amoebas and their total bulk
>    doubles each second.  In one hour the jar is full.
>    When is the jar half full?
>
> I post this puzzle for your entertainment.
>
> [-Rick-]

I guess this is set up to make students think in other than canned ways 
to solve problems.

It might be interesting to note that for the amoeba to take an hour to 
fill the jar by doubling it's volume each second, it would have to be 
far smaller than a proton.

-- 

Rick

tim <tim@seemywebsite.com> wrote:

(snip)

> Except that one didn't involve subatomic amoebas.

And since no-one answered the question I put up previously,
some amoeba have 670 gigabase pair genome, or about 220 
times the size of our genome. 

http://www.genomenewsnetwork.org/articles/02_01/Sizing_genomes.shtml

As for actual times, it takes E.coli 40 minutes to duplicate its DNA,
though it can divide every 20 minutes. (It has to start the next
duplication before the first one is finished.) E.coli is about 4.1
megabase pairs, so the amoeba has about 160,000 times more DNA
to copy. 

It seems that actual amoeba division takes between 4 and 33 hours.

-- glen

On Tuesday, September 30, 2014 2:17:45 PM UTC+13, Rick Lyons wrote:
> Hi Guys,
> 
>    My daughter is under the impression that I know 
> 
> something about mathematics.  In an e-mail she sent 
> 
> me the following puzzle:
> 
> 
> 
>   An amoeba is placed in an empty jar.  In one second 
> 
>   the amoeba splits into two amoebas, each as big as 
> 
>   the mother amoeba.  After another second the daughter 
> 
>   amoebas split in the same way.  As each new generation 
> 
>   splits, the number of amoebas and their total bulk 
> 
>   doubles each second.  In one hour the jar is full.  
> 
>   When is the jar half full?
> 
> 
> 
> I post this puzzle for your entertainment.
> 
> 
> 
> [-Rick-]

after 1 hour there will be this amount


5104866514341945590710842651568281920101670963940301617298884589783947025654989209426383867325613524543351416833597764127456946916446081781809010549986553357741499190223136441251634489586652942274537384864347088262714867022887786366083090924141383506229439852977377003900548348898351843259305917045924853771632524370243927651743845488737416874805848368486492650738383584061192790228759690288354373732123915430018234619975254042908858938625059308072478312356363081018346276548919002917583248151532523790105677074132985556300525623246994398997696641975576343860751434216573702938766124166198630901624439464793581607521987353750595573887822793123705818050746432686022104079817609890994191214546801218255872018703385608345194043092491620892210302046725582683029489136603774682567680282632685757711764405303795386293220314902546474539632698134739750566765427099848313932256081872633513314483128831881481867184896549309061788140015231068341421962504120281883042706210346559274047369836280866215728520613525447857373937770199894887258997449658106174721909842993657489968700917291224846565376

On 9/30/2014 12:09 PM, glen herrmannsfeldt wrote:
> tim <tim@seemywebsite.com> wrote:
>
> (snip)
>
>> Except that one didn't involve subatomic amoebas.
>
> And since no-one answered the question I put up previously,
> some amoeba have 670 gigabase pair genome, or about 220
> times the size of our genome.
>
> http://www.genomenewsnetwork.org/articles/02_01/Sizing_genomes.shtml

Yeah but it is likely full of non-encoding junk... much like ours.

-- 

Rick

On Mon, 29 Sep 2014 22:37:04 -0400, rickman <gnuarm@gmail.com> wrote:

>On 9/29/2014 9:17 PM, Rick Lyons wrote:
>>
>>
>>
>> Hi Guys,
>>     My daughter is under the impression that I know
>> something about mathematics.  In an e-mail she sent
>> me the following puzzle:
>>
>>    An amoeba is placed in an empty jar.  In one second
>>    the amoeba splits into two amoebas, each as big as
>>    the mother amoeba.  After another second the daughter
>>    amoebas split in the same way.  As each new generation
>>    splits, the number of amoebas and their total bulk
>>    doubles each second.  In one hour the jar is full.
>>    When is the jar half full?
>>
>> I post this puzzle for your entertainment.
>>
>> [-Rick-]
>
>I guess this is set up to make students think in other than canned ways 
>to solve problems.
>
>It might be interesting to note that for the amoeba to take an hour to 
>fill the jar by doubling it's volume each second, it would have to be 
>far smaller than a proton.
>
>-- 
>
>Rick

That makes some assumptions about the size of the jar.


Eric Jacobsen
Anchor Hill Communications
http://www.anchorhill.com

rickman <gnuarm@gmail.com> wrote:

(snip, I wrote)

>> And since no-one answered the question I put up previously,
>> some amoeba have 670 gigabase pair genome, or about 220
>> times the size of our genome.

>> http://www.genomenewsnetwork.org/articles/02_01/Sizing_genomes.shtml
 
> Yeah but it is likely full of non-encoding junk... much like ours.

Seems that the latest is that more of the "junk" than previously
thought actually does something. 

Protein coding sequences were the first discovered and understood,
but gene regulation is also coded in the DNA, and is taking longer
to understand.

In the case of bacteria, being able to divide faster is an 
evolutionary advantage, and so they tend to make more efficient
use of their genome. 

But otherwise, evolution mostly works by duplication and modification,
so having unused copies of genes lying around is useful. 

But yes, presumably much of the amoeba genome isn't doing anything.
If it doesn't cost a lot to keep it around, there isn't a big
incentive to reduce it.

-- glen