Professor Layton and the Diabolical Box

Puzzle 054: Painting the Flag

Original diagram for Puzzle 054: Painting the Flag

How many different flags can you make by colouring three stripes with three paints, without neighbouring stripes matching?

Chapter
Chapter 2
Location
Wheat Field · Kostya
Picarats
25 picarats
Type
Write Answer
Region
Same in all versions
Hint 1: A gentle nudge. Tap to flip.
Hint 1

Are you sure you only have three colours to work with?

Tap to flip back
Hint 2: The key idea. Unlocks after the previous card is flipped.
Hint 2

Nobody says every section has to be painted.

Tap to flip back
Hint 3: Almost there. Unlocks after the previous card is flipped.
Hint 3

Count white as a fourth colour. Pick the left stripe first, then each next stripe only has to differ from its neighbour.

Tap to flip back
Answer: See the answer. Unlocks after the previous card is flipped.
Answer

The answer is 36.

Tap to flip back
Solution, FAQ and sources

Solution

The flag starts out white, and leaving a section unpainted is allowed, so you really have **four** colours: the three paints plus white.

1. Left section: any of 4 colours. 2. Middle section: anything except the left colour, so 3 choices. 3. Right section: anything except the middle colour, so 3 choices.

4 × 3 × 3 = **36** designs.

About this puzzle

A white flag is split into three sections side by side. You have three paints, can’t mix them, and no two neighbouring sections can be the same colour. How many different flag designs are possible?

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

Similar puzzles: Puzzle 055: Sammy's Necklace, Puzzle 059: A Ticket to Where?, Puzzle 060: Plaza Puzzle, Puzzle 047: The Mayoral Election

All Professor Layton and the Diabolical Box puzzles

FAQ

What is the answer to Puzzle 054, Painting the Flag, in Professor Layton and the Diabolical Box?

The answer is 36.

Where do you find Puzzle 054 in Diabolical Box?

Puzzle 054 appears in Chapter 2, in the Wheat Field area, when you talk to Kostya.

How many picarats is Diabolical Box Puzzle 054 worth?

25 picarats.

Sources

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.