2020 AMC 10 B
Complete problem set with solutions and individual problem pages
There are people standing equally spaced around a circle. Each person knows exactly ' of the other Gpeople: the " people standing next to her or him as well as the person directly across the circle. How many ways are there for the people to split up into pairs so that the members of each pair know each other?(2020 AMC 10B, Question #17)
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Let us use casework on the number of diagonals. Case diagonals There are ways: either pairs with pairs with , and so on or pairs with pairs with , etc.
Case diagonal There are possible diagonals to draw (everyone else pairs with the person next to them. Note that there cannot be diagonals. Case diagonals Note that there cannot be a case with diagonals because then there would have to be diagonals for the two remaining people, thus a contradiction. Case diagonals There is way to do this. Thus, in total there are possible ways.
