Professor Layton and the Diabolical Box
Puzzle 047: The Mayoral Election
Three rival candidates and 40 voters in all: what's the fewest votes that guarantees a win?
- Chapter
- Chapter 2
- Location
- Town Hall Plaza
- Picarats
- 25 picarats
- Type
- Write Answer
- Region
- Same in all versions
Hint 1: A gentle nudge. Tap to flip.
Half of 40 is 20. Is that enough, or do you need 21?
Tap to flip backHint 2: The key idea. Unlocks after the previous card is flipped.
The candidates dislike each other. Who will each of them vote for?
Tap to flip backHint 3: Almost there. Unlocks after the previous card is flipped.
Each candidate is a guaranteed vote for themselves. How many votes can the strongest rival collect at most?
Tap to flip backAnswer: See the answer. Unlocks after the previous card is flipped.
The answer is 20 votes.
Tap to flip backSolution, FAQ and sources
Solution
The candidates can't stand each other, so each one votes for themselves (this is the assumption the game makes).
1. Suppose the leader gets 20 votes. That leaves 20 for the other two, and the third candidate has at least their own vote, so the closest rival has at most 19. The leader wins. 2. With only 19, a rival could reach 20 (40 − 19 − 1 for the third candidate), so 19 isn't safe.
The fewest votes for a certain win is **20**. (Without the self-vote assumption you'd need 21 to rule out a 20–20 tie.)
About this puzzle
Three candidates who can’t stand each other run for mayor in a town of 40 voters, including the candidates themselves. Everyone casts one vote, and the winner is whoever gets the most. What’s the smallest number of votes that guarantees victory?
Unofficial fan guide, not affiliated with LEVEL-5 or Nintendo. Puzzle description, hints and solution written by Hint by Hint.
Similar puzzles: Puzzle 054: Painting the Flag, Puzzle 055: Sammy's Necklace, Puzzle 038: Moving Day, Puzzle 044: Tangled Ropes
All Professor Layton and the Diabolical Box puzzles
FAQ
What is the answer to Puzzle 047, The Mayoral Election, in Professor Layton and the Diabolical Box?
The answer is 20 votes.
Where do you find Puzzle 047 in Diabolical Box?
Puzzle 047 appears in Chapter 2, in the Town Hall Plaza area.
How many picarats is Diabolical Box Puzzle 047 worth?
25 picarats.
Sources
- Professor Layton Wiki (Fandom): Puzzle:The Mayoral Election
- StrategyWiki: Professor Layton and the Diabolical Box/Puzzles 26-50
- Professor Layton Wiki (Fandom): Module:PuzzleData/DB
Facts checked on November 14, 2026
Unofficial fan guide. Not affiliated with, endorsed by, or sponsored by LEVEL-5 Inc. Professor Layton, The New World of Steam, and all related names, characters, and trademarks are the property of their respective owners.