1i ve solved it but by using symmetry
not directly
In a troop of 2008, 12 are on patrol duty every night. prove that it is impossible to draw up a schedule according to which every two are on duty exactly once
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5 Answers
1you see let us assume first that the schedule is possible
then no. of pairs (total)=2008C2=1004*2007
each day no. of mutual pairs = 12C2=11*6
but as each pair is together only once
hence total number of nights on duty =
1004*2007/6*11
but then it is coming out to be a fraction!!!
so not possible
