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The Mayoral Election is a puzzle in Professor Layton and the Diabolical Box.

Puzzle

US Version

Three people at odds with one another are running for mayor in the upcoming town election. Including these three candidates, the town has a voter population of 40 people. In order to win, a candidate must get more votes than any other candidate.

If each of the 40 voters casts a single vote and every vote is recognized, what is the fewest number of votes a candidate needs to secure victory with certainty?

UK Version

Three people at odds with one another are running for mayor in the upcoming town election. They are all locals of the town, which has a voter population of 40. In order to win, a candidate must get more votes than any other candidate.

If each of the 40 voters casts a single vote and every vote is recognised, what is the fewest number of votes a candidate needs to secure victory?

Hints




Click a Tab to reveal the Hint.

US Version

Think about how many votes exist in the town, excluding the three cast by the candidates themselves.

UK Version

Think about how many votes will be cast in the town excluding the three cast by the candidates themselves.

US Version

Even the three candidates themselves have the right to vote.

Of course, seeing as how each of them want to win, it's a given that the candidates will likely vote for themselves.

UK Version

The three candidates themselves also have the right to vote.

Of course, since each of them wants to win, you can take it for granted that each candidate will vote for themselves.

US Version

Forty votes, minus the three votes cast by the candidates, leaves you with 37 votes.

Find the number of votes it takes to gain a majority in a pool of 37 voters, and add one additional vote to that sum to get your answer.

UK Version

40 votes minus the three votes cast by the candidates leaves you with 37 votes.

Find the number of votes it takes to gain a majority in a pool of 37 voters and add one additional vote to that sum to get your answer.


Solution

Incorrect

Too bad!

Think hard about the clues you've been given and try again.

Correct

That's right!

US Version

The winner has to have at least 20 votes for a certain victory. Since each of the candidates dislikes the other two, each will likely vote for themselves. Forty votes minus those three votes leaves 37 votes. The winner will need over half the votes--in this case, a minimum of 19 additional votes. Add the winning candidate's personal vote to that, and you get 20 votes. Even if another candidate gathered all the remaining 18 votes, it wouldn't be enough to overcome the candidate with 20 votes.

UK Version

The winner needs at least 20 votes.

Since each of the candidates dislikes the other two, they will probably all vote for themselves. 40 votes minus those three votes leaves 37 votes. The winner will need over half the votes, or 19. Add the winning candidate's personal vote to that and you get 20 votes. Even if another candidate gathered all the remaining 18 votes, that wouldn't be enough to overcome the candidate with 20 votes.

DB047S

A big thanks to http://professorlayton2walkthrough.blogspot.com

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