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Ahmes's Papyrus


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#1 rookie1ja

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Posted 30 March 2007 - 03:52 PM

Ahmes's Papyrus - Back to the Cool Math Games
About 1650 B. C., Egyptian scribe Ahmes, made a transcript of even more ancient mathematical scriptures dating to the reign of the Pharaoh Amenemhat III. In 1858 Scottish antiquarian, Henry Rhind came into possession of Ahmes's papyrus. The papyrus is a scroll 33 cm wide and about 5.25 m long filled with math riddles. One of the problems is as follows:
100 measures of corn must be divided among 5 workers, so that the second worker gets as many measures more than the first worker, as the third gets more than the second, as the fourth gets more than the third, and as the fifth gets more than the fourth. The first two workers shall get seven times less measures of corn than the three others.
How many measures of corn shall each worker get? (You can have fractional measures of corn.)

This old topic is locked since it was answered many times. You can check solution in the Spoiler below.
Pls visit New Puzzles section to see always fresh brain teasers.


Spoiler for Solution


Spoiler for old wording

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#2 Veracity

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Posted 17 May 2007 - 03:18 PM

[quote="rookie1ja":f0981]
Ahmes's Papyrus - Back to the Logic Puzzles
About 2000 B. C. there lived Ahmes, a royal secretary and mathematician of the Pharaoh Amenemhat III. In 1853 an Englishman Rhind found one of Ahmes's papyruses near the temple of Ramses II. in Thebes. The papyrus is a rectangle 33 cm wide and about 5 m long. There is the following math brain teaser on it (besides others).
100 measures of corn must be divided among 5 workers, so that the second worker gets as many measures more than the first worker, as the third gets more than the second, the fourth more than the third and the fifth more than the fourth. The first two workers shall get seven times less measures of corn than the three others.
How many measures of corn shall each worker get?


Ahmes's Papyrus - solution
2 equations give a clear answer to the given question:
5w + 10d = 100
7*(2w + d) = 3w + 9d
Where w is amount of corn for the first worker, d is the difference (amount of corn) between two consecutive workers. So this is the solution:
1st worker = 10/6 measures of corn
2nd worker = 65/6 measures of corn
3rd worker = 120/6 (20) measures of corn
4th worker = 175/6 measures of corn
5th worker = 230/6 measures of corn
[/quote]


Yeah, That's what I was gunna say! LMAO

There is another way to get the answer aswell! Check it out. It's using a new and highly unique system for mathematical equations. It's called Veracity-ism-atics. Let me show you how it works...


Ahmes's Papyrus - solution
2 equations give a clear answer to the given question:
5w + 10d = 100
7*(2w + d) = 3w + 9d
Where w is amount of corn for the first worker, d is the difference (amount of corn) between two consecutive workers. So this is the solution:
1st worker should have shot the second worker and taken his corn. Doing so would have increased his 10/6 measure of corn to 75/6.
2nd worker (being DeaD to the 4th power would have bled on the 3rd workers 120/6 making it useless for consumption = an extra bag of funky, yet washable corn to the 70-teenth square root of the space time vortex. NOW, if you measures of corn using the square root of how confussed I am at this very moment, the 5th worker will call it a day and get social services to cut him some food stamps, and buy the whole block some Government Cheese wasting 45.832 units of Stampageary thingys because he could have used Jose's next door neighbors dogs Masters uncles WIC check instead making much more sence to Anyone with Any type of Education, DUHHH..

Now you have one guy with corn, One guy with a block of cheese, and me feeling like a complete moron who should have stayed in school instead of smoking all the weed at 15 years old... LMAO
3rd worker = 120/6 (20) measures of corn
4th worker = 175/6 measures of corn
5th worker = 230/6 measures of corn[/quote]
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#3 Naruki

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Posted 12 August 2007 - 12:29 AM

Ahmes's Papyrus
So this is the solution:
1st worker = fractional measure of corn
2nd worker = fractional measure of corn
3rd worker = whole measure of corn
4th worker = fractional measure of corn
5th worker = fractional measure of corn



I think this solution will not work, since it is quite right to assume they would not give out pieces of corn with any kind of mathematical precision. If fractions are to be considered, that would be extraordinary, and should have been explicitly stated in the puzzle.

The ear of corn itself must be the irreducible smallest unit. As such, it is impossible to divide 100 ears amongst 5 workers in the given scenario.
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#4 KBHoleN1

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Posted 28 August 2007 - 04:33 PM

I took a slightly longer way to get it, but the principle was the same as the 2 simple equations. Assigning a formula to each individual difference (as in x=b-a=c-b etc...) and some fun algebraic substitutions, I arrived at the 4th worker receiving 175/6 pieces of corn as well.

Naruki's point about fractional corn is well-taken, but the puzzle is fun nonetheless.
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#5 credels

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Posted 16 October 2007 - 09:49 PM

The answer is NONE. Corn wasnt used by Egyptians until the 15th century.
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#6 rookie1ja

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Posted 16 October 2007 - 11:26 PM

The answer is NONE. Corn wasnt used by Egyptians until the 15th century.

well, a few sources prove the opposite

what is your source?
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#7 credels

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Posted 16 October 2007 - 11:36 PM

doh!
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#8 Rembu

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Posted 22 October 2007 - 05:29 PM

I have to agree with credels. I read your sources and didn't quite understand how it could be possible, unless corn can be many things. Sorry, English is not my dominant language, but whenever I read corn I think maize. So, if corn is maize Egyptians could not have had it any earlier than Polish had potatoes.
I think that in the sources you had there might have been a translation problem. I did not even see a picture of corn on any of them. It should be common knowledge that corn was brought to Europe by the conquistadors.
Here are sources for everyone:

First one is type origin of corn on google.
Purdue University
CampSilos
The corn war - competing theories on the origin of corn, Discover, Dec 1997, C Dold.

If any of these are right, then credel is right as well.

Other than that the teaser was pretty fun.
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#9 Aryous1024

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Posted 07 November 2007 - 05:27 PM

The answer is actually like this :

The first man has 20
The second man has 20
The third man has 20
The fourth man has 20
and the fifth man has 20

because they all have 0 more than the next, and they all have an actual amount of corn, not fractions of corn.
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#10 Andrew

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Posted 28 November 2007 - 04:43 AM

The answer is actually like this :

The first man has 20
The second man has 20
The third man has 20
The fourth man has 20
and the fifth man has 20

because they all have 0 more than the next, and they all have an actual amount of corn, not fractions of corn.



Except that 40 is not seven times less than 60. So it doesn't meet the final line:
"The first two workers shall get seven times less measures of corn than the three others."

And I agree, that the puzzle should be edited to say that you can have fractional measures of corn. At first I didn't think I had the right answer because I thought that you should be coming out with a whole number.

But I had a lot of fun with the puzzle nonetheless (equation rearrangement up the wazoo!!)

Oh, and I'm new. Howdy everyone!!
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