



 
Hi Jacey, It can. When the number of people is even, each month everyone meets someone. When it is odd, some person has a month off every so often. Let's suppose the number of people is even. Number them 0, 1, ..., 2n2 and infinity. In week 1, the pairs are {infinity, 0}, {1, 2n2}, {2, 2n3}, ..., {n1, n}. For each subsequent week, add one to each number with the two conditions that infinity + 1 = infinity, and (2n2) + 1 = 0. This will give each possible pairing exactly once over 2n1 weeks, and then it will repeat. When the number of people is odd, go up to the next even number, and adopt the rule that whomever is scheduled to meet person 0 has that week off. Hope this helps.  


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