Answer to Question #262187 in Discrete Mathematics for abhi

Question

 The federal Green Party recently elected a new leader: Bernie May. A party official said 23,877 Green voters cast a ballot in this race. If the voters were partitioned into 12 regions based on population, give a proof by contradiction that at least one region had at least 1990 voters.

Answer 1

Let us prove by contradiction. Suppose that in each region the number of voters is less than $1990.$ Therefore, in all 12 regions we get at most $12\cdot 1989=23,868$ voters. Since $23,868<23,877$ we have a contradiction. This contradiction proves that at least one region had at least $1990$ voters.