Guest Posted June 30, 2009 Report Share Posted June 30, 2009 how can fifteen girls walk in five rows of three each for seven days so that no girl walks with any other girl in the same row (triplet) more than once? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted June 30, 2009 Report Share Posted June 30, 2009 As long as they are not confined to their original columns, there are many possibilities Quote Link to comment Share on other sites More sharing options...
0 Guest Posted June 30, 2009 Report Share Posted June 30, 2009 (edited) well, many orders, but one final conclusion. I am to lazy to work it out, but i am sure there is only one true answer that can be arranged any number of ways. Edited June 30, 2009 by King Arcon Quote Link to comment Share on other sites More sharing options...
0 Prof. Templeton Posted July 1, 2009 Report Share Posted July 1, 2009 Day 1:"ABC", "DEF", "GHI", "JKL", "MNO" Day 2:"ADG", "BEJ", "CFM", "HKN", "ILO" Day 3:"AEN", "BDO", "CHL", "FIK", "GJM" Day 4:"AIM", "BGL", "CDK", "EHO", "FJN" Day 5:"AHJ", "BKM", "CEI", "DLN", "FGO" Day 6:"AFL", "BIN", "CJO", "DHM", "EGK" Day 7:"AKO", "BFH", "CGN", "DIJ", "ELM" Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 1, 2009 Report Share Posted July 1, 2009 Day 1:"ABC", "DEF", "GHI", "JKL", "MNO" Day 2:"ADG", "BEJ", "CFM", "HKN", "ILO" Day 3:"AEN", "BDO", "CHL", "FIK", "GJM" Day 4:"AIM", "BGL", "CDK", "EHO", "FJN" Day 5:"AHJ", "BKM", "CEI", "DLN", "FGO" Day 6:"AFL", "BIN", "CJO", "DHM", "EGK" Day 7:"AKO", "BFH", "CGN", "DIJ", "ELM" I'm assuming that's right, but I couldn't find a systematic method for working this out. How did you do it? Quote Link to comment Share on other sites More sharing options...
0 Prof. Templeton Posted July 2, 2009 Report Share Posted July 2, 2009 I'm assuming that's right, but I couldn't find a systematic method for working this out. How did you do it? The sub-patterns may be easier to see this way: 15 girls #,A,B,C,D,E,F,G,a,b,c,d,e,f,g Day 1: "#Aa", "EGf", "CDg", "BFd", "bce" Day 2: "#Bb", "FAg", "DEa", "CGe", "cdf" Day 3: "#Cc", "GBa", "EFb", "DAf", "deg" Day 4: "#Dd", "ACb", "FGc", "EBg", "efa" Day 5: "#Ee", "BDc", "GAd", "FCa", "fgb" Day 6: "#Ff", "CEd", "ABe", "GDb", "gac" Day 7: "#Gg", "DFe", "BCf", "AEc", "abd" Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 4, 2009 Report Share Posted July 4, 2009 If the rows are reversed each day no one would ever be in the same row. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 7, 2009 Report Share Posted July 7, 2009 This took me a long time, I started by figuring out how many ways the girls could be paired, (0 with 1-E, 1 with 2-E, 2 with 3-E, ect..). Then I applied this same method to triplets (0 with pairs 1X+, 1 with pairs 2X+) but only using each pair once, I was able to eleminate conflicts as I went. This gave me the 35 groups, arranging the 35 groups into 7 days was done by trial and error, but didnt take to long and it all fell together. 012 37B 49E 5AC 68D 034 18A 2BE 57D 69C 056 1BD 289 3AE 47C 078 1CE 245 39D 6AB 09A 135 2CD 48B 67E 0BC 179 58E 236 4AD 0DE 146 59B 27A 38C probably not the most logical approach, but I enjoyed it. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 1, 2009 Report Share Posted August 1, 2009 (edited) A bit of history here. The problem is known as "Kirkman's Schoolgirl Problem," invented by T.P. Kirkman and published in The Lady's and Gentleman's Diary for 1850. No answer is trivial, but Frost's "General Solution and Extension of the Problem of the 15 Schoolgirls," Quarterly Journal of Pure & Aplied Mathematics, vol. XI, 1871, and B. Pierce's "Cyclic Solutions of the School-girl Puzzle," The Astronomical Journal, vol. VI, 1859 - 1861, are considered among the more elegant solutions. Edited August 1, 2009 by jerbil Quote Link to comment Share on other sites More sharing options...
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how can fifteen girls walk in five rows of three each for seven days so that no girl walks with any other girl in the same row (triplet) more than once?
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