Puzzle 105 is Free Lunch!, a 30-picarat Multiple Choice puzzle at the City Monument in Monte d'Or, in Chapter 7. Firth, an old man from a village across the desert, offers it as one of the puzzles expeditions used to pass the time on the trek. Three colleagues, A, B and C, spin a wheel with segments worth 1, 2 and 3 points six times, and the one with the fewest points pays for lunch. You only know A's total, and you have to work out who paid.
This page covers story Puzzle 105 in Professor Layton and the Miracle Mask, the 3DS game (US and UK English). The wheel and the answer are the same in the US and UK English versions; quotes use the North American text. If you're after Daily Puzzle 105 or Puzzle 105 from another Layton game, see Wrong Puzzle 105? below.
What Puzzle 105 is
| Name | Free Lunch! (US and UK) |
|---|---|
| Type | Multiple Choice |
| Picarats | 30 |
| Location | City Monument, Monte d'Or |
| Chapter | Chapter 7 |
| How you start it | Talk to Firth |
| Required? | No |
| Previous puzzle number | Puzzle 104, Undercover Code (Dalston Parlor) |
| Next puzzle number | Puzzle 106, Confusion Cubed (Merchant District) |
The puzzle reads: "Every day colleagues A, B, and C spin a wheel to determine who will pay for lunch. The wheel is divided into three segments worth the number of points indicated in the picture. They spin the wheel six times. Each time, all three of them receive points according to which segment lands on them. Whoever has the fewest total points at the end has to pick up the bill." Then it asks: "Today, A has ended up with 13 points. If no two people finished with the same score, who had to pay for lunch?" The objective bar says "Who pays for lunch today?"
The top screen shows the wheel with A, B and C sitting around it. The three segments always keep the same order as the wheel turns, so once you know which segment lands on one person, you know what the other two get on that spin. The touch screen has a portrait button for each of the three. Touch the one you think paid.
Puzzle names
| Version | Puzzle name |
|---|---|
| North America | Free Lunch! |
| UK | Free Lunch! |
| Japanese | ゴチそう勝負 (Gochi-sō Shōbu, "the treat-or-be-treated contest") |
The name is the same in the US and UK versions. The UK text has a few small wording differences: it says "got" for "gotten", writes "Lazy Susan" with a capital L and "everyone's score", and places some commas differently. The wheel and the answer are the same in the US and UK English versions.
Wrong Puzzle 105?
- Daily Puzzle 105 is Flight 04, from the Aerial View set.
- Puzzle 104, Undercover Code, is the puzzle before this one, hidden in a book in Dalston Parlor. If yours is about a novel with no page numbers, that's the one you've got.
- Puzzle 106, Confusion Cubed, is the next puzzle, in the Merchant District. If yours has six maze panels to fold into a cube, that's the one you've got.
- Puzzle 105 in another Layton game is a different puzzle. If yours doesn't show a points wheel and three colleagues, you're in the wrong game.
Where you find it
Chapter 7 opens on the fourth day of the investigation in Monte d'Or, in Layton's Room at the Dromedary, where Emmy asks, "Where should we start today, Professor?" Go to the City Monument and talk to Firth, the old man standing by the arcade on the left of the square.
Firth remembers, "When I was young, this area was sand. All sand. Just sand." Luke says, "It's hard to believe this was just part of the desert 18 years ago." Firth goes on, "I've seen many expeditions that moved their camp from my village to this town," and "As they trekked across the desert, they'd bring puzzles to help pass the time." Then the puzzle starts.
You don't have to solve it to move on. Firth keeps offering it for the rest of Chapter 7, and he's back at the City Monument with it after the story ends.
When the scores get confusing
- You don't know where to start. A's 13 points are the only number you're given. List every way six spins of 1, 2 and 3 can add up to 13, the way Hint 1 suggests.
- You're not sure what B and C get. The three segments stay in the same order, so each value A gets fixes what the other two get on that spin. Read it off the wheel in the picture.
- Two cases look possible. Remember that no two people finished with the same score. Rule out any case where B or C also ends on 13.
- The game says "Too bad." The wrong-answer message is "Too bad. You should be able to work out everyone's scores based on A's." You can try again.
- You can't find the puzzle. Talk to Firth at the City Monument during Chapter 7.
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 from A
The only score you know is A's: 13 points. To get this many points after six spins of the wheel, she could have gotten two points on five occasions and three points once, for example.
What other combinations of points would give A a score of 13?
Hint 2: three ways to make 13
There are only three ways for A to have received 13 points after six spins.
1 x 3 pts., 5 x 2 pts. = 13 pts.
2 x 3 pts., 3 x 2 pts., 1 x 1 pt. = 13 pts.
3 x 3 pts., 1 x 2 pts., 2 x 1 pt. = 13 pts.
Now you can look at the wheel and work out how many points B and C would have received in each of these cases.
Hint 3: B's and C's scores
Did you work out B's and C's scores in each of the cases outlined in Hint 2?
When A gets 1, B gets 3. When A gets 2, B gets 1. When A gets 3, B gets 2. C gets the remaining points in each case.
Oh, and don't forget that no two people got the same number of points, so you can rule out any combination that gives B or C the same score of 13 that A has.
Super Hint: the one case left
There are three ways for A to receive 13 points, and you can exclude any case in which B or C also gets 13 points.
There's only one way left, and that leaves A with 13 points, B with 7, and C with 16.
The one with the fewest points pays for lunch.
Answer and full solution
The answer below names who paid, works out all three possible score sheets and shows the finished puzzle. Open it when you're ready.
Show the answer
Answer: B. Touch B's portrait.
On every spin, the three segments go to the three people together. When A gets 1, B gets 3 and C gets 2. When A gets 2, B gets 1 and C gets 3. When A gets 3, B gets 2 and C gets 1. Each spin hands out 1 + 2 + 3 = 6 points, so after six spins the three totals always add up to 36.
| Case | A | B | C | Result |
|---|---|---|---|---|
| One 3 and five 2s | 13 | 2 + 1 + 1 + 1 + 1 + 1 = 7 | 1 + 3 + 3 + 3 + 3 + 3 = 16 | All different |
| Two 3s, three 2s and one 1 | 13 | 2 + 2 + 1 + 1 + 1 + 3 = 10 | 1 + 1 + 3 + 3 + 3 + 2 = 13 | C ties with A, ruled out |
| Three 3s, one 2 and two 1s | 13 | 2 + 2 + 2 + 1 + 3 + 3 = 13 | 1 + 1 + 1 + 3 + 2 + 2 = 10 | B ties with A, ruled out |
Only the first case fits: A has 13, B has 7 and C has 16. B has the fewest points, so B pays for lunch.
The game confirms it: "Correct! B lost out and had to pay for everyone. Spin, spin, spin! Don't you find yourself wanting to spin the lazy Susan when you get one at the restaurant?"
If it still doesn't work out:
- You chose C. C has the most points in the only case that works, 16.
- You chose A. A's 13 is in the middle. B's 7 is lower.
- You stopped at the first case you found. Check all three cases. Two of them give someone else 13, which the question rules out.
Picarats, hints and hint coins
Free Lunch! shows 30 picarats when it starts. The puzzle can award 30, 20 or 10 picarats. Wrong answers may reduce the picarat value. A wrong answer brings the message "Too bad. You should be able to work out everyone's scores based on A's." When you talk to Firth again, he says, "That puzzle was a classic for the explorers." before the puzzle starts again.
Hints cost hint coins, not picarats. Hints 1 to 3 cost one hint coin each and the Super Hint costs two, five in total. The hints on this page are free to open.
Does it unlock anything?
It doesn't give you an item. You get the picarats, and the puzzle counts toward your total.
Versions
- Nintendo 3DS family: this page covers the 3DS game. The wheel is on the top screen, and you touch your answer on the touch screen.
- US and UK English versions: the wheel and the answer are the same in the US and UK English versions. The UK text differs in some wording.
The scene around the puzzle
If you quit the puzzle, Firth grumbles, "Mmph. I guess that one wasn't so good for passing much time..."
When it's solved, Firth recalls, "I remember when travelers needed to find a spring to make it across the desert," and "We've got a river back home. It comes from the spring here in Monte d'Or." Luke asks, "There must be an underground waterway flowing through this area, then?" Firth answers, "That's right! It's all connected. Everything is connected if you think about it. My beard may be connected to the parade here!" and Luke sighs, "I didn't see this conversation going into philosophical matters of facial hair..."
FAQ
Where is the answer to Puzzle 105?
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.
What is Puzzle 105 called?
Free Lunch!, in both the North American and UK versions. In Japanese it's ゴチそう勝負.
Where is Puzzle 105?
At the City Monument in Monte d'Or, in Chapter 7, on the fourth day of the investigation. Talk to Firth.
Do I have to solve Puzzle 105?
No. The story doesn't need it.
Can I fail Puzzle 105?
Yes. A wrong choice brings "Too bad.", and you can try again as many times as you need. Wrong answers may reduce the picarat value.
How many picarats is Puzzle 105 worth?
It shows 30 picarats when it starts. The puzzle can award 30, 20 or 10 picarats. Wrong answers may reduce the picarat value.
Is Daily Puzzle 105 the same as Puzzle 105?
No. It's a different puzzle, listed under Wrong Puzzle 105?. Story Puzzle 105 is the lunch wheel puzzle at the City Monument.
More Miracle Mask puzzles
- Puzzle 104: Undercover Code
- Puzzle 106: Confusion Cubed
- Puzzle 103: Stars of the Stage
- Puzzle 102: Dice Crates
- Puzzle 101: Wonky Wiring
- Puzzle 100: Gate to the Ruins!
- Puzzle 60: Dangerous Holes
- Puzzle 113: Chip Champions
- Puzzle 118: Evenly Matched 3
- Puzzle 122: Kitty Solitaire 3
For the rest of the game's puzzles, see the Miracle Mask puzzle index.