rookie1ja 11 Report post Posted March 30, 2007 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. 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. Share this post Link to post Share on other sites

Guest Report post Posted May 17, 2007 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 Share this post Link to post Share on other sites

Guest Report post Posted August 11, 2007 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. Share this post Link to post Share on other sites

Guest Report post Posted August 28, 2007 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. Share this post Link to post Share on other sites

Guest Report post Posted October 16, 2007 The answer is NONE. Corn wasnt used by Egyptians until the 15th century. Share this post Link to post Share on other sites

rookie1ja 11 Report post Posted October 16, 2007 The answer is NONE. Corn wasnt used by Egyptians until the 15th century. well, a few sources prove the opposite what is your source? Share this post Link to post Share on other sites

Guest Report post Posted October 22, 2007 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. Share this post Link to post Share on other sites

Guest Report post Posted November 7, 2007 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. Share this post Link to post Share on other sites

Guest Report post Posted November 28, 2007 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!! Share this post Link to post Share on other sites

rookie1ja 11 Report post Posted November 28, 2007 puzzle edited ... stating that "you can have fractional measures of corn" Share this post Link to post Share on other sites

Guest Report post Posted November 30, 2007 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. Share this post Link to post Share on other sites

Guest Report post Posted December 6, 2007 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. Here's a site that talks about Egyptian bread: http://www.touregypt.net/featurestories/bread.htm Share this post Link to post Share on other sites

Guest Report post Posted January 10, 2008 (edited) 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 January 10, 2008 by miya Share this post Link to post Share on other sites

Guest Report post Posted January 21, 2008 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 Share this post Link to post Share on other sites

Guest Report post Posted February 15, 2008 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. Share this post Link to post Share on other sites

rookie1ja 11 Report post Posted February 15, 2008 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 ...) Share this post Link to post Share on other sites

Guest Report post Posted February 15, 2008 i wouldnt divide the corn i'd eat it Share this post Link to post Share on other sites

Guest Report post Posted March 13, 2008 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 :-( Share this post Link to post Share on other sites

Guest Report post Posted March 20, 2008 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. Share this post Link to post Share on other sites

Guest Report post Posted April 9, 2008 A=2.5 B=10 C=15 D=32.5 E=40 Share this post Link to post Share on other sites

Guest Report post Posted April 23, 2008 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... Share this post Link to post Share on other sites

Guest Report post Posted May 16, 2008 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. Share this post Link to post Share on other sites

Guest Report post Posted January 23, 2009 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 Share this post Link to post Share on other sites

Guest Report post Posted November 28, 2009 (edited) 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 November 28, 2009 by Spacepeet Share this post Link to post Share on other sites