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In The Still Of The Night

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HistoricFoodie View Drop Down
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    Posted: 29 September 2013 at 00:47
It's the mid-watch; the graveyard shift, the witching hours. Call it what you will, we're talking about the still of the night, the hours between midnight and dawn, when nothing is happening, and your mind wanders.

Tonight I'm wandering towards that old culinary saw:

If a hen and a half 
Lays an egg and a half
In a day and a half
How many eggs will six hens lay in six days?

We've all heard it. But did you know there are three radically different answers, each of which is 100% correct?

It's true. The correct response depends on whether you're a normal person, a mathamatition, or a chef.

So, just for giggles, and because I'm bored to tears, I thought we could have fun discussing what the answers are, how they're derived, and what relevance this has to the kind of cooking we do. 
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TasunkaWitko View Drop Down
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Post Options Post Options   Thanks (0) Thanks(0)   Quote TasunkaWitko Quote  Post ReplyReply Direct Link To This Post Posted: 29 September 2013 at 11:09
this should be interesting!
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Rod Franklin View Drop Down
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Rod Franklin Quote  Post ReplyReply Direct Link To This Post Posted: 29 September 2013 at 11:41
If 1.5 hens lay 1.5 eggs in 1.5 days, then twice as many hens (3 hens) would lay twice as many eggs (3 eggs) in the same amount of time (1.5 days) and twice as many again (6 hens) would lay twice as many eggs (6 eggs) in again, the same amount of time (1.5 days.) 4 times 1.5 days equals 6 days, so 4 times 6 eggs gives me the answer of 24 eggs laid by 6 hens in 6 days.

I got lost for awhile by multiplying the days right along with the hens and eggs...

So, what are the other ways of figuring this?


 
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Post Options Post Options   Thanks (0) Thanks(0)   Quote AK1 Quote  Post ReplyReply Direct Link To This Post Posted: 29 September 2013 at 17:47
I say 36. A hen lays an egg every day. 6 hens times 6 days.  36 eggs.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Rod Franklin Quote  Post ReplyReply Direct Link To This Post Posted: 29 September 2013 at 18:37
How do you figure one hen, one egg, one day?
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Post Options Post Options   Thanks (0) Thanks(0)   Quote HistoricFoodie Quote  Post ReplyReply Direct Link To This Post Posted: 29 September 2013 at 23:03
I knew this would get a fight going. Evil Smile

Just for the record, both figures are right. 

The way he gets the one-hen, one-egg result, Rod, is that he thinks in logical, as opposed to mathematical,  terms.

Mathematically, we are dealing in sets, as you identified. The sets, in this case, are 1 1/2. There are, as you've shown, four sets in six days, and four x six is 24.

Darko, on the other hand, is reasoning that if 1 1/2 hens lay 1 1/2 eggs in 1 1/2 days, that is the same, proportionately, as 1 hen laying one egg in one day. And thus, 6 (the number of hens) x 6 (the number of days) equals 36.

So, that's two of the three. Who's ready to tell us the third correct response?
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Addtotaste Quote  Post ReplyReply Direct Link To This Post Posted: 30 September 2013 at 04:21
BACON!
 
Party
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Post Options Post Options   Thanks (0) Thanks(0)   Quote HistoricFoodie Quote  Post ReplyReply Direct Link To This Post Posted: 30 September 2013 at 08:47
Close, Hila, but no cigar!
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Post Options Post Options   Thanks (0) Thanks(0)   Quote pitrow Quote  Post ReplyReply Direct Link To This Post Posted: 30 September 2013 at 09:01
I'm with Rod, though I got to it slightly differently, but still mathematically.

If a hen and a half lays and egg and a half, then each hen lays one egg.

They lay an egg each 1.5 days. So over six days a hen would lay 4 eggs (6/1.5 = 4).

6 hens would then make 24 eggs in 6 days (6x4 = 24)
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Post Options Post Options   Thanks (0) Thanks(0)   Quote TasunkaWitko Quote  Post ReplyReply Direct Link To This Post Posted: 30 September 2013 at 09:32
I say 36, simply because half a hen can't lay half an egg, even if it is a zombie chicken. With that, all the "halves" are summarily discarded.
 
1 egg per day = 6 eggs in 6 days; times 6 hens =36. The halves are simply hanging out in the fridge, waiting to be cooked.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote pitrow Quote  Post ReplyReply Direct Link To This Post Posted: 30 September 2013 at 11:18
Originally posted by TasunkaWitko TasunkaWitko wrote:

I say 36, simply because half a hen can't lay half an egg, even if it is a zombie chicken. With that, all the "halves" are summarily discarded.
 
1 egg per day = 6 eggs in 6 days; times 6 hens =36. The halves are simply hanging out in the fridge, waiting to be cooked.


But you can't quite discount the half a day. The half a hen and half an egg yes, but the half day needs to be accounted for.  If it takes 36 hours for a hen to produce and egg, then by discarding that half day, your numbers are skewed.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote TasunkaWitko Quote  Post ReplyReply Direct Link To This Post Posted: 30 September 2013 at 11:25
But, Mike - it doesn't take a hen 36 hours to produce an egg. It takes a hen AND A HALF a day AND A HALF to produce an egg AND A HALF. Given that, by the time 24 hours have passed, the hen has produced an egg and the half a hen is evidently working on the half an egg.
 
I got to thinking about this, and if a person wanted to add the halves back in, shouldn't the total eggs be 54? This would be 36 x 1.5, which in theory would account for all of the halves that I discarded.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Rod Franklin Quote  Post ReplyReply Direct Link To This Post Posted: 30 September 2013 at 12:12
The halves are inconvenient numbers when dealing with live hens and fresh eggs.

So our first inclination is to change the hen and egg numbers to make the whole problem easier to understand by arriving at whole hen and whole egg numbers. In the end we're after what 6 hens can do. Let's start by finding out what 6 hens can do in 1.5 days. Starting at 1.5 of each of hens and eggs, it's easy to see that we would need to multiply the hen and egg numbers by 4 to find out what happens with 6 hens in 1.5 days.

Doing the multiplication results in 4 X 1.5hens = 6 hens laying 4 X 1.5eggs = 6 eggs in 1.5 days.

The original question wants to know what can happen in 6 days. Just like before 4 X 1.5 = 6. So multiplying what 6 chickens can do in 1.5 days by 4 results in the only real answer, which is 24.

The one chicken, one egg, one day thing is the key to the confusion. To get rid of those inconvenient chicken and egg numbers, it's easy to want to double everything and say 3 chickens lay 3 eggs in 3 days, which when broken down from there to a one chicken statistic gives 1 chicken, 1 egg, 1 day, but it's wrong to alter the time involved when simplifying the .5 chickens and .5 eggs away.

I'm just explaining what I already covered...
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Post Options Post Options   Thanks (0) Thanks(0)   Quote TasunkaWitko Quote  Post ReplyReply Direct Link To This Post Posted: 30 September 2013 at 12:23
Not to throw a monkey wrench into the works, but I see that the question asks: How many eggs will six hens lay in six days?
 
Notice the six hens and six days - the actual question itself doesn't mention the halves, even though they are prominently mentioned when setting up the trick?question.
 
Things like this are exactly why my degree is in History and not Math....or anythng related at all to Math.....
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Post Options Post Options   Thanks (0) Thanks(0)   Quote TasunkaWitko Quote  Post ReplyReply Direct Link To This Post Posted: 30 September 2013 at 13:41
If a half a hen laid half an egg in half a day, how much would a pint of butter weigh?
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Post Options Post Options   Thanks (0) Thanks(0)   Quote pitrow Quote  Post ReplyReply Direct Link To This Post Posted: 30 September 2013 at 16:12
lol Ron, reminds me of this...


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Post Options Post Options   Thanks (0) Thanks(0)   Quote TasunkaWitko Quote  Post ReplyReply Direct Link To This Post Posted: 30 September 2013 at 16:15
that right there is my entire life when it comes to math.....
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Post Options Post Options   Thanks (0) Thanks(0)   Quote HistoricFoodie Quote  Post ReplyReply Direct Link To This Post Posted: 30 September 2013 at 22:51
Ron, a pint is a liquid measure.

So, if we melt the butter, and assume (not a good idea) that butter and water have the same specific gravity, then a pint of butter will weigh one pound---cuz a pints a pound the world around. If you're talking about water. A pint of iron bbs would weigh considerably more. 

But you can't quite discount the half a day

But that's exactly what you did, Mike.  According to you, each hen lays one egg. But you missed the point that they do it in one day. So, by doing the conversion to whole hens, the answer should be 36---each hen lays one egg in one day, times six. 
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Post Options Post Options   Thanks (0) Thanks(0)   Quote africanmeat Quote  Post ReplyReply Direct Link To This Post Posted: 30 September 2013 at 23:45
I am with rod.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Addtotaste Quote  Post ReplyReply Direct Link To This Post Posted: 30 September 2013 at 23:50
Butter is one baking item that has the same weight as volume. I.E. if a recipe says 250ml butter you can put in 250g butter.
 
(I did very well in Home Ec and avergage in standard grade maths so I am just deflecting)
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