Professor Layton and the Diabolical Box

Puzzle 014: Red Caps

Ten children get red or other caps, and only some of them win red balloons, so how many balloons were red?

Chapter: Chapter 1
Location: Car 5 (Dining Car)
Picarats: 25 picarats
Type: Write Answer
Region: Same in all versions

Hint 1: A gentle nudge. Tap to flip.

Hint 1

Nobody can see their own cap. Think about what a red-capped child sees compared with everyone else.

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Hint 2: The key idea. Unlocks after the previous card is flipped.

Hint 2

If there were lots of red caps, everybody would see at least four. That can't be right.

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Hint 3: Almost there. Unlocks after the previous card is flipped.

Hint 3

Try exactly four red caps. What do the red-capped children see, and what do the others see?

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Answer: See the answer. Unlocks after the previous card is flipped.

Answer

The answer is 6.

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Solution, FAQ and sources

Solution

Suppose *r* children have red caps. A red-capped child sees *r* − 1 red caps; any other child sees *r*.

1. If *r* is 5 or more, every child sees at least 4, so everyone gets a red balloon. But only some did. 2. If *r* is 3 or fewer, nobody sees 4, so nobody gets one. 3. So *r* = 4. The four red-capped children see only 3 and get blue balloons; the other six see 4 and get red ones.

Red balloons: **6**.

About this puzzle

A teacher secretly puts a cap on each of ten children. Anyone who can see four or more red caps on the others gets a red balloon; everyone else gets a blue one. Only some of the children end up with red balloons. How many red balloons were handed out?

Unofficial fan guide, not affiliated with LEVEL-5 or Nintendo. Puzzle description, hints and solution written by Hint by Hint.

All Professor Layton and the Diabolical Box puzzles

FAQ

What is the answer to Puzzle 014, Red Caps, in Professor Layton and the Diabolical Box?

The answer is 6.

Where do you find Puzzle 014 in Diabolical Box?

Puzzle 014 appears in Chapter 1, in the Car 5 (Dining Car) area.

How many picarats is Diabolical Box Puzzle 014 worth?

25 picarats.

Sources

Professor Layton Wiki (Fandom): Puzzle:Red Caps
StrategyWiki: Professor Layton and the Diabolical Box/Puzzles 1-25
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.