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Painting the Flag is a puzzle in Professor Layton and the Diabolical Box.

Puzzle

US Version

You have a pristine white flag that you want to color into three sections as shown below. You have three paints.

No two adjacent sections of the flag can be the same color, each section can be only one color, and you can't change the number or size of these sections.

If you aren't allowed to mix paint, how many distinct flag designs are possible?

UK Version

You have a pristine white flag that you want to dye into three sections as shown below. You have three dyes.

No two adjacent sections of the flag can be the same colour, each section can only be one colour and you can't change the number or size of these sections.

If you aren't allow to mix the dyes, how many distinct flag designs are possible?

Hints




Click a Tab to reveal the Hint.

US Version

You have three paints you can use on the flag, but that doesn't mean those are the only colors at your disposal.

UK Version

You have three dyes you can use on the flag, but that doesn't mean those are the only colours at your disposal.

US Version

Maybe you've noticed that the white color of the flag's fabric is another color you can use in making your designs.

UK Version

Maybe you've noticed that the white colour of the flag's fabric is another colour you can use in making your designs.

US Version

Adding white to the three paints you have gives you four colors you can use to make flag designs.

If the leftmost third of your flag is white, you will have a total of nine distinct designs.

UK Version

Adding white to the three dyes you have, there are four colours you can use to make flag designs.

If the left section of your flag is red, for example, then combining the other two dyes and the flag's own white colour in the remaining two sections gives you a total of nine distinct designs.


Solution

Incorrect

Too bad!

US Version

Think hard about the clues you've been given and try again.

UK Version

Give the puzzle another try.

Correct

Sharp thinking!

US Version

Once you incorporate the white color of the unpainted flag into your designs, you actually have four colors to the left third of the flag and list all designs possible, you get a total of nine variations.

Multiply this number by four, which represents the number of colors at your disposal, to get the answer: 36 variations.

UK Version

Once you incorporate the white colour of the unpainted flag into your designs, you actually have four colours you can work with. If you assign a colour to the left section of the flag and list all designs possible, you get a total of nine variations.

Multiply this number by four, which represents the number of colours at your disposal, to get the answer: 36 variations.

DB054S

A big thanks to http://professorlayton2walkthrough.blogspot.com

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