# Professor Layton and the Diabolical Box

## Question from lentels

### Can someone explain puzzle 54 for me?

I know that the answer to the painting the flag puzzle (puzzle 54) is 36, but how can you solve that puzzle without actually writing out the 36 combinations?

6 years ago

## Answers

**TheGuidingLight answered:**

The game's own solution explains this fairly well (by working out 9 combinations and multiplying by 4)

Saying that, the puzzle can be solved without having to work out any specific combinations

The left third of the flag can be any of 4 possibilities

As the middle third must be different from the left third, the middle third can only be any of 3 possibilities (for each of the 4 possibilities for the left third)

As the right third must be different from the middle third, this third can also only be any of 3 possibilities (for each of the 3 possibilities for the middle third)

From this, working out the number of possible combinations is simply 4x3x3

For easy reference, the puzzle, hints and solution can be seen here

professorlayton2walkthrough.blogspot.com/2008/11/puzzle054.html

6 years ago

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