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A Lick of Paint is a puzzle in Professor Layton and the Miracle Mask. The puzzle must be solved in order to progress the story.

## Puzzle

The prospective tenants of this row of houses have some unusual requirements.
1. "I want to live next to a red house!"
2. "No blue neighbors, please. Oh, and a house on the end is out of question!"
3. "Two doors down from a yellow house, and no neighbors the same color as us!"
4. "I'm fine with any color as long as it's not blue or red!"

Can you repaint just one house so that every tenant can have their dream home? Touch a house to change its color.

## Hints

Click a Tab to reveal the Hint.

You can reduce the complexity of this puzzle by thinking about how the tenants' requirements limit the houses they can move into. For example, 2 doesn't want to be on the ends of the row, so the only choices are house B or house C.

Now take a look at 2's other requirement, and see which of those two houses would be the correct one.

Let's suppose 2 moves into house B. That would require house C to be repainted.

If you paint C red, that leaves A as the only house that A could move into (neither red or blue). 3 then has to move into either house C or house D, but neither satisfies the requirements. So house C can't be painted red.

Continuing the line of thought from Hint 2, let's say 2 still moves into house B, but this time you paint house C yellow. That means that 1 and 3 can take house A or C, leaving house D for 4. However, house D doesn't satisfy 4's requirements.

So out of the two houses, B and C, that 2 could move into, there is no way to repaint C and make everyone happy. Thus 2 has to take house C.

From the previous hints, you know that 2 moves into house C. This leaves no house that 3 can move into, unless one of either B or D is painted yellow.

Painting B yellow would let 3 move into house D, but then there would be no red house for 1 to live next door to.

Only one possibility remains.

## Solution

### Incorrect

Take another look at the tenants' conditions, and see whose house color and position you can work out for certain.

### Correct

Correct!

Repainting the rightmost house in yellow satisfies all the tenants' conditions.

Never mind the cost of materials and labor--the landlord ought to charge all four of them for the time it took to work out which house to paint!