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 September 13th, 2015, 11:21 AM #1 Banned Camp   Joined: Dec 2013 Posts: 1,117 Thanks: 41 Hard puzzle We have 252 5-uples extracted from 10 numbers (1 to 10). C(10,5)=252 We want to place them under constraint around a circular table. Definition 1 : Two 5-uples are called brothers if they share 4 numbers. Example : 1-2-3-4-5 and 1-2-3-4-10 are brothers. Each 5-uple has 25 brothers (C(5,4)*(C(5,1)). Brotherhood is not transitive : A=1-2-3-4-5 B=1-2-3-4-6 C=1-2-3-6-7 A is brother of B but not brother of C B is brother of A and brother of C C is brother of B but not of A Definition 2 : We call distance d the number of seats at left and at right of some 5-uple sitting around the table. Example : d=5 We count 5 seats at left and 5 seats at right of a sitting 5-uple. The challenge is to place all the 252 5-uples around a circular table such as if we choose any 5-uple no brother will be sitting at the distance d with d maximal. Example : if the maximal value is 8 then any 5-uple out of the 252 will NOT have a brother sitting at the distance 8. What is the value of d? What are the seats choosen for the 252 5-uples or in other words how are they going to be placed?
 September 14th, 2015, 03:47 PM #2 Banned Camp   Joined: Dec 2013 Posts: 1,117 Thanks: 41 Almost solved! Without computer...

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