



 
It cannot start any later than the 10th month, because there are only nine others to observe. It can start that late. Arrange them (on paper) in a circle. In month N, each person observes the person N after them. This does mean that, in month 5, pairs are observing each other, and in several months there are two cycles of length 5. Is this a problem? I can see how to get eight months of 10cycles: for instance: ABCDEFGHIJA and reverse; But I suspect nine (or N1 for any even N?) is impossible.  


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