Professor Layton and the Curious Village

Puzzle 016: Triangles and Ink

Original diagram for Puzzle 016: Triangles and Ink

One pen dip draws a four-triangle shape, so how many dips draw a big triangle of 36 little ones?

Chapter
Chapter 2
Location
Town Hall · Rodney
Picarats
40 picarats
Type
Write Answer
Region
Same in all versions
Hint 1: A gentle nudge. Tap to flip.
Hint 1

36 ÷ 4 = 9 is the obvious answer, and it's wrong.

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

Look closely at the four-triangle shape. How many triangles do you actually draw?

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

The middle triangle appears for free once the three around it are drawn. Count the upward-pointing triangles in the big shape.

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

The answer is 7 dips.

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Solution, FAQ and sources

Solution

1. The four-triangle shape is really three upward-pointing triangles. The fourth, upside-down one in the middle appears on its own once the other three are drawn. So one dip draws **three upward triangles**. 2. The big shape is a triangle six small triangles along each side, giving 36 small triangles: 21 pointing up (1 + 2 + 3 + 4 + 5 + 6) and 15 pointing down. 3. Draw only the 21 upward triangles and all the downward ones appear automatically.

21 ÷ 3 = **7** dips.

About this puzzle

One dip of your pen gives enough ink to draw a small shape made of four little triangles. How many dips do you need to draw a big triangle made of 36 little triangles?

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

Similar puzzles: Puzzle 013: Sinking Ship, Puzzle 011: Arc and Line, Puzzle 021: Pill Prescription, Puzzle 009: One Poor Pooch

All Professor Layton and the Curious Village puzzles

FAQ

What is the answer to Puzzle 016, Triangles and Ink, in Professor Layton and the Curious Village?

The answer is 7 dips.

Where do you find Puzzle 016 in Curious Village?

Puzzle 016 appears in Chapter 2, in the Town Hall area, when you talk to Rodney.

How many picarats is Curious Village Puzzle 016 worth?

40 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.