Guest Posted July 2, 2008 Report Share Posted July 2, 2008 YOU HAVE 81 GOATS, EACH GOAT HAS UNIQUE No. 1 TO 81, (No. IS NOT REPEATED). GOAT GIVES MILK ACCORDING TO THEIR No. FOR EXAMPLE No.1 Goat =1 Ltr. Milk. No.2 Goat = 2 Ltr. Milk. No.3 Goat = 3 Ltr. Milk. """ = "" """ = "" "" = "" "" = "" "" = "" "" = "" No. 81 Goat = 81 Ltr Milk NOW QUESTION IS TOTAL GOATS HAVE TO DISTRIBUTED TO 9 PERSONS IN SUCH A MANNER THAT EACH PERSON GETS EQUAL NUMBER OF GOATS AND EQUAL MILK. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 2, 2008 Report Share Posted July 2, 2008 The only way to get equal number of goats for each person would be to divide it by 9 ==> 81 / 9 = 9 goats. This isn't the answer but how can you get an equal number of goats for 9 people. Dividing is only way. Unless....could you have decimal or fractions?? Quote Link to comment Share on other sites More sharing options...
0 grey cells Posted July 2, 2008 Report Share Posted July 2, 2008 9 goats and 369 litres for each person . Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 2, 2008 Report Share Posted July 2, 2008 (edited) :lol:I got 369 litres for each person and 9 goats. Simple. Edited July 2, 2008 by SillouhetteMind Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 2, 2008 Report Share Posted July 2, 2008 Yes, of course, that's just arithmetic. But the question is, what is the allocation of goats? This would be easy if the numbers were 8 and 64, but with 9 and 81 it is more complicated. Quote Link to comment Share on other sites More sharing options...
0 grey cells Posted July 2, 2008 Report Share Posted July 2, 2008 Yes, of course, that's just arithmetic. But the question is, what is the allocation of goats? This would be easy if the numbers were 8 and 64, but with 9 and 81 it is more complicated. Yes , I get you . The allocation is much more difficult , so I slipped in the easier part. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 2, 2008 Report Share Posted July 2, 2008 1 11 21 31 41 51 61 71 81 2 12 22 32 42 52 62 72 73 3 13 23 33 43 53 63 64 74 4 14 24 34 44 54 55 65 75 5 15 25 35 45 46 56 66 76 6 16 26 36 37 47 57 67 77 7 17 27 28 38 48 58 68 78 8 18 19 29 39 49 59 69 79 9 10 20 30 40 50 60 70 80 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 2, 2008 Report Share Posted July 2, 2008 (edited) 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 work in mod 9 except express 0(mod 9) as 9(mod 9) now all the people have to get 369 liters of milk. so the first person gets a diagonal of the above grid going from the top left to the bottom right. the next person gets a diagonal directly to the left with 9 being "left" of 1. The patterns continues in that manner. This way the first person gets the 369 total liters and the next person gets 8 goats that produce one less liter than a specific goat of the previous person and 1 goat that produces 8 more liters than a specific goat of the previous person. *That "mapping" is bijective* Edited July 2, 2008 by wfwood Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 2, 2008 Report Share Posted July 2, 2008 Since 1+2+3+......+81 = 3321. Average milk volume per person should be 3321/9 = 369 liters And since each person should have 9 goats, the simple way is to list down the number by 1 to 9th in each rows like below: 1.....2.....3.....4.....5.....6.....7.....8.....9 10...11...12...13...14...15....16...17...18 19...20...21...22...23...24...25....26...27 28...29............................................. ...................................................... 73...74...75...76...77....78..79....80...81 then you use the pencil to make a line diagonally from 1, 11, 21, 31, 41, .....71, 81 and all these 9 number add up to be 369 then the second line will be from 2, diagonally draw through 12, 22, 32,........72, and drop at the space right after 81, then move 73 beside 81 again. So 73th will be the last number for group 2. By drawing every line diagonally and get all the 9 numbers, you will have the summation of each group = 369 Answer: Group 1: 1, 11, 21, 31, 41, 51, 61, 71, 81 Group 2: 2, 12, 22, 32, 42, 52, 62, 72, 73 Group 3: 3, 13, 23, 33, 43, 53, 63, 64, 74 Group 4: 4, 14, 24 ,34, 44, 54, 55, 65, 75 Group 5: 5, 15, 25, 35, 45 ,46, 56, 66, 76 Group 6: 6, 16, 26, 36, 37, 47, 57, 67, 77 Group 7: 7, 17, 27, 28, 38, 48, 58, 68, 78 Group 8: 8, 18, 19, 29, 39, 49, 59, 69, 79 Group 9: 9, 10, 20, 30, 40, 50, 60, 70, 80 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 2, 2008 Report Share Posted July 2, 2008 It seems that some of you are on the right track to find the answer. Its Like Solving a SUDOKU. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 3, 2008 Report Share Posted July 3, 2008 Nobody has got the right answer yet Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 3, 2008 Report Share Posted July 3, 2008 Nobody has got the right answer yet You mean Sonny d and I didn't answer correctly? Quote Link to comment Share on other sites More sharing options...
0 Yoruichi-san Posted July 3, 2008 Report Share Posted July 3, 2008 You mean Sonny d and I didn't answer correctly? I think there is more than one possible answer...it's basically a latin square...using the 9 by 9 matrix you guys created, as long as each person gets only one number from each row and each column, it works... Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 3, 2008 Report Share Posted July 3, 2008 (edited) The Answer is persons: 1st 2nd 3rd 4th 5th 6th 7th 8th 9th goats: 1 2 3 4 5 6 7 8 9 18 10 11 12 13 14 15 16 17 26 27 19 20 21 22 23 24 25 34 35 36 28 29 30 31 32 33 42 43 44 45 37 38 39 40 41 50 51 52 53 54 46 47 48 49 58 59 60 61 62 63 55 56 57 66 67 68 69 70 71 72 64 65 74 75 76 77 78 79 80 81 73 Edited July 3, 2008 by Mr.G Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 3, 2008 Report Share Posted July 3, 2008 I think there is more than one possible answer...it's basically a latin square...using the 9 by 9 matrix you guys created, as long as each person gets only one number from each row and each column, it works... Yoruichi san ga tadashi desu Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 3, 2008 Report Share Posted July 3, 2008 I think there is more than one possible answer...it's basically a latin square...using the 9 by 9 matrix you guys created, as long as each person gets only one number from each row and each column, it works... Agree! In fact we can get the answer same as what Mr. G's one if we pick from the 9x9 matrix the number from rightmost top to leftmost bottom. Apparently Sonny d and I start from leftmost top to rightmost bottom. Quote Link to comment Share on other sites More sharing options...
Question
Guest
GOAT GIVES MILK ACCORDING TO THEIR No.
FOR EXAMPLE
No.1 Goat =1 Ltr. Milk.
No.2 Goat = 2 Ltr. Milk.
No.3 Goat = 3 Ltr. Milk.
""" = ""
""" = ""
"" = ""
"" = ""
"" = ""
"" = ""
No. 81 Goat = 81 Ltr Milk
NOW QUESTION IS
TOTAL GOATS HAVE TO DISTRIBUTED TO 9 PERSONS IN SUCH A MANNER THAT EACH PERSON GETS EQUAL NUMBER OF GOATS AND EQUAL MILK.
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