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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 5uples 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 5uples are called brothers if they share 4 numbers. Example : 12345 and 123410 are brothers. Each 5uple has 25 brothers (C(5,4)*(C(5,1)). Brotherhood is not transitive : A=12345 B=12346 C=12367 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 5uple sitting around the table. Example : d=5 We count 5 seats at left and 5 seats at right of a sitting 5uple. The challenge is to place all the 252 5uples around a circular table such as if we choose any 5uple no brother will be sitting at the distance d with d maximal. Example : if the maximal value is 8 then any 5uple 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 5uples 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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