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Ahmes's Papyrus

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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.

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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

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?

Edit: you can have fractional measures of corn.

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• 1 month later...

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

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

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• 2 months later...
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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• 3 weeks later...

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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• 1 month later...

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

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

well, a few sources prove the opposite

doh!

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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.

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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• 3 weeks later...

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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• 3 weeks later...
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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puzzle edited ... stating that "you can have fractional measures of corn"

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I don't know about anyone else, but I arrived at the correct answer in a different fashion. My algebra skills are probably a little rusty but here's how I went about it.

A represents worker 5

X represents the constant distance between the amount of corn that each worker has more than the last.

A + (A-X) + (A-2X) + (A-3x) + (A-4x) = 100

7(A-3X + A-4X) = A + (A-X) + (A-2X)

Some of this has some similarities to the above solution obviously. This is actually the extended expression of what is in the solution above. I simplified it in a very different fashion, which wasn't near as simple, perhaps.

If you solve for X in the second expression your end result is as follows:

A = X*46/11

With that in mind, I replaced all instances of A with X*46/11 and solved for X.

X = 9.16667 (55/6)

A = 55/6 * 46/11 OR 5/6 * 46 = 38.3333...

Obviously from there, you can deduce the rest and the results are identical. I have a feeling that I did this the hard way.

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credels is correct. Corn (maize) is a New World grain, completely unknown to the ancient Egyptians. In earlier Modern English, the word "corn" was a synonym for "grain"; thus, for example, in the King James Bible, we read about "ears of corn", which really means "heads of grain". The grain (or "corn") raised by the Egyptians consisted mainly of wheat, with some barley also raised on occasion.

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• 1 month later...

1st worker = 1.66666 measures of corn

2nd worker = 10.83333 measures of corn

3rd worker = 20 measures of corn

4th worker = 29.16666 measures of corn

5th worker = 38.3333 measures of corn

Edited by miya
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• 2 weeks later...

1 worker : 1 1/3 m.

2 worker : 10 5/6 m

3 worker : 20m

4 worker : 32 1/2m

5 worker : 238 1/3m

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• 4 weeks later...
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?

Edit: you can have fractional measures of corn.

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

I suck at math but I love Logic problems. I can't stand fractions so my answer may be worng as ever but this seems quite simple. If you split up 100 measures of corn amongst 5 poeple and the first person has to have less than the second an so on but also have 7 times less than the 5th person than wouldn't the outcome look like this:

1st person- 5 measures of corn

2nd person- 10 measures

3rd- 20 measures

4th- 30 measures

5th 35 measures.

That all adds up to 100 and 35 divided by 5 is 7, right? Which makes the first person having 7x less than the 5th.

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I suck at math but I love Logic problems. I can't stand fractions so my answer may be worng as ever but this seems quite simple. If you split up 100 measures of corn amongst 5 poeple and the first person has to have less than the second an so on but also have 7 times less than the 5th person than wouldn't the outcome look like this:

1st person- 5 measures of corn

2nd person- 10 measures

3rd- 20 measures

4th- 30 measures

5th 35 measures.

That all adds up to 100 and 35 divided by 5 is 7, right? Which makes the first person having 7x less than the 5th.

that does not work because there are various differences between the workers (1st vs. 2nd = 5 measures, but 2nd vs. 3rd = 10 measures ...)

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i wouldnt divide the corn i'd eat it

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• 4 weeks later...
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?

Edit: you can have fractional measures of corn.

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

If the 7 were changed to 3, ie. "The first two workers shall get THREE times fewer measures of corn than the three others.", then the consequence will be an integer solution requiring no corn-chopping. NINE works too, but leaves the first worker without corn -- not fair :-(

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If the 7 were changed to 3, ie. "The first two workers shall get THREE times fewer measures of corn than the three others.", then the consequence will be an integer solution requiring no corn-chopping. NINE works too, but leaves the first worker without corn -- not fair :-(

Nice work belwood. I like the idea of making it an integer solution. Even though cleaning it up makes it seem easier it's still a fun puzzle.

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• 3 weeks later...

A=2.5

B=10

C=15

D=32.5

E=40

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• 2 weeks later...

I don't see what the problem with fractions in this question is. The riddle says 100 measures of corn, not 100 ears of corn or 100 kernels of corn. A measure is an arbitrary unit until the unit is defined. For all we know the 'measure' could be 'a dozen ears' which, when used in the fractions would yield whole ears of corn. Or it could be volume equivalents, etc...

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• 4 weeks later...

First 4.1667

Second 8.3333

Third 12.5

Fourth 25

Fifth 50

So, First and Second together add up to 12.5 The other three add up to 87.5 which is 7x12.5

Second is twice First. Third is twice Second. Fourth is twice Third and Fifth is twice Fourth.

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• 8 months later...

if you give workers the same amount it works out completly the same way as the others without the unlogical fractoins! 0x1=0x2=0x3=0x4=0x5=0x6=0x7

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• 10 months later...

Love the comments about dealing 20,20,20,20,20... can't ppl read the line 'the first two get seven times less than the last three'!!

Edited by Spacepeet
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This topic is now closed to further replies.