Puzzle 039 is A Hat of Tiles, a 30-picarat tile puzzle from Michelle, the receptionist at City Hall, in Chapter 3. It's optional. You get twelve square tiles, each 3 by 3 squares: eight white, three black and one red. Lay them one on top of another inside a 7 by 7 frame so the finished picture matches the top hat on the top screen. A tile you lay later covers whatever is under it, so the whole puzzle is about the order.
This page covers story Puzzle 039 in Professor Layton and the Miracle Mask on Nintendo 3DS (US and UK English), using the North American text. If you're after Daily Puzzle 039, one of the other tile puzzles or Puzzle 39 from another Layton game, see Wrong Puzzle 039? below.
What Puzzle 039 is
| Name | A Hat of Tiles (the same in the US and UK English versions) |
|---|---|
| Type | Tile |
| Picarats | 30 |
| Location | Reception, City Hall, Monte d'Or |
| Chapter | Chapter 3 |
| Given by | Michelle, the City Hall receptionist |
| Required for the story? | No |
| Previous puzzle number | Puzzle 038, Pattern Pending (One-Ring Circus) |
| Next puzzle number | Puzzle 040, Crossed Connections (Reception) |
Reading the question
The puzzle says: "You have a stack of thin tiles that are 3 x 3 in size. There are three colors, and each tile is a solid color. Use the available tiles and stack them on top of each other to construct a top hat like the one above. How should you layer them? Take the tiles from the right and place them inside the border on the left." The objective bar says, "Make the hat!"
The top screen shows a girl in a top hat sitting on a bench in a garden. Behind her, a wall of 7 by 7 square tiles shows the hat: a black crown, a red band, a black brim five squares wide, and white all around it. On the touch screen, the empty frame is on the left and the tiles are on the right, with a count next to each pile: eight white, three black and one red.
The text calls the colors white, black and red. On the screen they may look cream, dark brown and orange, so you may see those names used instead. They're the same tiles.
How stacking works
Drag a tile from a pile into the frame. Each tile covers a 3 by 3 block of the frame's squares, and the pile's count goes down by one. When one tile overlaps another, the one you laid later sits on top and hides the squares underneath. Only the top layer counts toward the picture.
That means you can't build the hat in whatever order you like. Twelve tiles of 9 squares cover far more than the frame's 49 squares, so most tiles end up partly hidden, and you have to work out which tile is underneath which. If the frame gets into a mess, tap Restart and lay the tiles again.
Puzzle names
| Version | Puzzle name |
|---|---|
| North America | A Hat of Tiles |
| UK English | A Hat of Tiles |
| Japanese | タイルで帽子 (Tairu de Bōshi, "a hat from tiles") |
The name is the same in the US and UK English versions. The UK English text probably words the question a little differently and uses British spellings such as "colours" and "centre." The tiles, the hat and the answer are the same in the US and UK English versions.
The Japanese title is タイルで帽子. The North American version carries a different Japanese label, ３色タイル.
Wrong Puzzle 039?
- Daily Puzzle 039 in Miracle Mask is a different puzzle: Streetlights 05, from the Bewitching Night set (it may also be listed as Bewitching Night 05).
- Puzzle 040, Crossed Connections, is also in Reception. It's a hidden puzzle that starts when you tap the lamp at the end of the counter. If your puzzle is about drawing lines, you've got that one.
- Michelle's later tile puzzles look a lot like this one. Puzzle 072, A Cup of Tiles, comes in Chapter 5 and Puzzle 112, A Duck of Tiles, in Chapter 7, both at Reception. Puzzle 136, A Pattern of Tiles, is one of Layton's Challenges. Check the number and the picture before you follow an answer.
- Puzzle 39 in another Layton game is a different puzzle. If yours doesn't show a top hat made of squares, you're in the wrong game.
Where you get it
Puzzle 039 comes in Chapter 3, on the second day of the investigation. After you've been to Dalston's mansion, the objective changes to "Check City Hall!" (or "Find the Mayor at City Hall!" if you've already solved 25 puzzles). Either way, go up City Hall Steps and into Reception. Michelle is the receptionist at the desk. She says, "Stamp and file, stamp and file. Every time the Masked Gentleman appears, the paperwork goes through the roof!" She grumbles about the police, "How do they expect to solve crimes when they can't even solve this puzzle?" and hands it to you.
If you quit, she says, "Well, you're just a citizen, so I don't expect you to be able to solve it." Talk to her again and she asks, "The police expect to solve crimes, and they can't even solve this puzzle?"
Mayor Billson is in the same room. He won't let you join the task force until you've solved at least 25 puzzles, so if you're short, Michelle's puzzle is one more toward that total.
Hint coins in Reception
Reception has four hint coins: on the light, on the box on top of the shelves, on the yellow notice and under the left-side chair.
Michelle's puzzle isn't required to move the story on. If you leave it unsolved, it probably goes to Nanna Grams (known as Elizabeth in the UK version) at the start of Chapter 5. It's simplest to solve it while you're at City Hall.
When the answer comes back wrong
- "That's a shame." That's the game's message for a wrong answer. It doesn't tell you which square is wrong, so compare your frame with the top screen square by square.
- The ends of the brim are white instead of black, or the other way round. The brim is five squares wide, but tiles are three wide. Think about which tiles have to go over the brim and which have to go under it.
- The red band has black or white squares in it. A tile laid after the red one is covering part of it. Look at which tiles overlap the band and when you lay them.
Hints, one at a time
These are the game's own hints, word for word from the North American version and in the same order. Open only the next one you need. In the game, Hints 1 to 3 cost one hint coin each and the Super Hint costs two.
Hint 1: Start at the edge
Each tile has a size of 3 x 3, and you can place tiles anywhere, but they have to run all the way around the edge. Start by placing the eight white tiles so they run around the edges.
Hint 2: The brim
Place the black tiles along the brim of the hat so that you end up with a 3 x 5 rectangle. Now we have the problem of how to make the sides of the brim look right. Although Hint 1 told you to place all the white tiles first, try bringing two of them to the front and see what you can do.
Hint 3: The tile that goes last
Do you now have a black, upside-down T shape? Look at the model to see how to proceed from here. There's a fully visible 3 x 3 black tile positioned at the top of the hat. That has to be the last tile you place.
Super Hint: The hatband
If the last tile to place is a black one, then the tile for the red of the hatband must come before it. Position it exactly in the center and then place the last black tile. You know where it goes.
Answer and full solution
The answer below covers every step, with pictures of the finished puzzle. Open it when you're ready.
Show the answer
Lay the tiles in five rounds: six white tiles around the top and bottom, two black tiles for the brim, two white tiles at the sides, the red tile in the center, and the last black tile on top of the red one. Then tap Submit.
| Order | Tile | Squares it covers |
|---|---|---|
| 1 to 3 | White ×3 (bottom corners and bottom middle) | Rows 5 to 7: columns 1 to 3, columns 3 to 5 and columns 5 to 7 |
| 4 to 6 | White ×3 (top corners and top middle) | Rows 1 to 3: columns 1 to 3, columns 3 to 5 and columns 5 to 7 |
| 7 and 8 | Black ×2 (the brim) | Rows 4 to 6: columns 2 to 4 and columns 4 to 6 |
| 9 and 10 | White ×2 (the sides) | Rows 3 to 5: columns 1 to 3 and columns 5 to 7 |
| 11 | Red | Rows 3 to 5, columns 3 to 5 (the exact center) |
| 12 | Black (the crown) | Rows 2 to 4, columns 3 to 5 |
Step by step:
- Six white tiles first. Put one in each of the four corners, one in the middle of the top edge and one in the middle of the bottom edge. Together they cover the top three rows and the bottom three rows. The middle row stays empty for now.
- Two black tiles for the brim. Lay them side by side, overlapping by one column, so their bottom row sits just above the bottom edge. They make a black block 3 squares tall and 5 wide, covering columns 2 to 6 of rows 4 to 6.
- Two white tiles at the sides. Put the last two white tiles in the middle of the left edge and the middle of the right edge. They cover the top two rows of the black block except the middle column, which leaves a black, upside-down T: the full brim along row 6 and a thin stem above it.
- The red tile in the center. Lay it exactly in the middle of the frame, on rows 3 to 5 and columns 3 to 5. Its bottom row becomes the hatband.
- The last black tile. Put it one row higher than the red tile, on rows 2 to 4 and columns 3 to 5. It covers the top two rows of red and becomes the crown. Only the red band in row 5 is left showing. Tap Submit.
The game says, "You did it! That's some expert tile laying right there!"
You have a little freedom. The six white tiles in step 1 can go down in any order, and the three along the top can wait until any time before the last black tile. The middle tiles on the top and bottom edges can also sit one column to the left or right, because the corner tiles still cover the rest of the edge. The order of the black, white, red and black rounds is the part that can't change.
If your answer keeps failing:
- Check the brim. If its ends are white, one of the bottom white tiles went down after the brim, so lay all three bottom white tiles before the black ones. If there's extra black on either side of the band or the crown, the side white tiles went down before the brim instead of after it.
- Check the band. If part of it is white, a side white tile was laid after the red tile. If it's missing, the last black tile is too low: it should cover rows 2 to 4, not 3 to 5.
- Count the piles. All twelve tiles are used, so every pile should be empty when you submit.
Picarats, hints and hint coins
A Hat of Tiles shows 30 picarats when it starts. Its three picarat values are all 30.
Hints cost hint coins, not picarats. The costs are one coin each for the first three hints and two for the Super Hint, five in total. The four coins in Reception don't quite cover all of them, so use the free hints on this page and save your coins.
Versions
- Nintendo 3DS family: this page covers the 3DS game. You drag the tiles with the stylus on the touch screen.
- US and UK English versions: same name, same tiles, same answer. The UK text uses British spellings.
The scene around the puzzle
Before the puzzle, Michelle complains, "All these officers, and they still can't catch the guy. What if I were that bad at my job? Just sayin'."
When it's solved, she says, "The police can't solve this puzzle that some ordinary citizen can! No wonder this investigation is going nowhere!" Layton answers, "To be fair, the Masked Gentleman's actions are highly unpredictable," and Emmy adds that with safety the top priority, it could be risky to take him into custody in a crowd. Michelle isn't impressed: "I've heard the excuses more times than you can imagine." She points you to the task force in the back meeting room, if you have the mayor's permission. Talk to her again afterwards and she says, "All these police officers do is stand around, eat scones, and talk about cricket."
FAQ
Where is the answer to Puzzle 039?
It's in the Answer and full solution section above, hidden until you open it. If you only want a push, open the hints one at a time first.
Where is Puzzle 039?
In Reception at City Hall, in Chapter 3. Talk to Michelle at the desk after the objective sends you to City Hall.
The hints say white, black and red, but my tiles look cream, brown and orange. Is that the same puzzle?
Yes. The hints call the colors white, black and red. On the screen they may look cream, dark brown and orange.
Do I have to solve Puzzle 039?
No. It's optional. If you skip it, it probably goes to Nanna Grams at the start of Chapter 5. It does count toward the 25 solved puzzles Mayor Billson asks for.
How many picarats is Puzzle 039 worth?
It shows 30 picarats when it starts. Its three picarat values are all 30.
Is Daily Puzzle 039 the same as Puzzle 039?
No. Daily Puzzle 039 is Streetlights 05, from the Bewitching Night set (it may also be listed as Bewitching Night 05). Story Puzzle 039 is Michelle's top hat tile puzzle.
More Miracle Mask puzzles
- Puzzle 038: Pattern Pending
- Puzzle 040: Crossed Connections
- Puzzle 037: Spin Shenanigans
- Puzzle 041: From the Sidelines
- Puzzle 035: Guess Stars
- Puzzle 034: The Cat's Trophy
- Puzzle 036: Going Dough-Nuts!
- Puzzle 042: Couple at the Café
- Puzzle 043: Evenly Matched
- Puzzle 044: Suit Crates
- Puzzle 045: From Left to Right
- Puzzle 022: Poke 'Em Totems
- Puzzle 60: Dangerous Holes
- Puzzle 100: Gate to the Ruins!
For the rest of the game's puzzles, see the Miracle Mask puzzle index.