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Today Puzzle #559

Puzzle No. 559 – Tuesday 3 September

With talk in the air of an early general election….Suppose the same number of people vote in each of Parliament’s 650 constituencies, and four candidates stand in each seat. To the nearest whole number….

a)What is the lowest possible percentage of the national vote that could give one party an overall majority of 326 seats?

b)What is the highest possible percentage that a party could obtain and NOT secure an overall majority?

Today’s #PuzzleForToday has been set by Peter Kellner former President of YouGov

Click here for the answer

a) 13%. Suppose one party wins no votes at all in 324 seats, but wins each of the other 326 by a single vote, with the other three parties all securing the same number of votes. Then its total vote is one vote over 25% in each of 50.15% of the seats (326 out of 650), This is fractionally over 12.5% of the total vote.

b) 75%. The party wins 324 seats with 100% of the vote. This gives it 49.85% of the total national vote. In the other 326, it is defeated by one vote by another party, with the remaining two parties winning no votes. This is one vote under 50% in 50.15% of the seats – or close to 25% of the national vote.

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