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'Voting Paradox' printed from https://nrich.maths.org/
How many different possible ways can each of the three voters
vote?
For a paradox we are looking for situations in which
(A beats B beats C beats A) or (B beats A beats C beats B) etc.
Try counting the number of ways in which such situations are
possible. To reduce the number of cases to analyse, you might
consider what happens if two voters agree on their first choice.