## 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?

This question is open with pending answers, but none have been accepted yet

STATUS

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

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