The winner is...
There is an election in Brillianopolis (population 600). There is a system where you can submit 5 votes to 1 party (1st), 3 votes to another (2nd), and 1 vote to a third party (3rd). There are 4 parties in Brillianopolis: Red, Green, Blue, and Yellow.
Most people like the Blue party , so 1/2 of the ballots look like this:
- 1st: Blue
- 2nd: Green
- 3rd: Red
But, some people like Green, so 1/3 of the ballots are like this:
- 1st: Green
- 2nd: Red
- 3rd: Blue
1/6 of the city are Yellow supporters. Their ballots looks like this:
- 1st: Yellow
- 2nd: Green
- 3rd: Blue
What is the sum of votes for the losing parties (that is all parties that don't get the most votes)?
The answer is 3200.
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First group of voters: ½ of 600, 300 voters.
-1st: Blue- 300×5= 1500 votes. -2nd: Green- 300×3= 900 votes. -3rd: Red- 300×1= 300 votes.
Second group of voters: ⅓ of 600, 200 voters.
-1st: Green- 200×5= 1000 votes. -2nd: Red- 200×3= 600 votes. -3rd: Blue- 200×1= 200 votes.
Third group of voters: ⅙ of 600, 100 voters.
-1st: Yellow- 100×5= 500 votes. -2nd: Green- 100×3= 300 votes. -3rd: Blue- 100×1= 100 votes.
All 600 people have voted, 300+200+100=600.
The winner party is clearly the Green party with 900+1000+300= 2200 votes, of a total vote provision of 600×(5+3+1)= 5400 votes.
The collective votes of the losing parties°= 5400-2200= 3200 votes.