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Splitting It Up is a puzzle in Professor Layton and the Curious Village.

Puzzle

You have a big wooden cube that's painted red on all six sides. After splitting the cube into smaller parts as shown below, you are left with 27 cubes identical in size but varying in the number of red sides per cube.

How many of these 27 small cubes have just one of their six sides painted red?

Hints




Click a Tab to reveal the Hint.

Take another look at the picture.

When this big cube is divided, which of the small cubes do you think will have one side painted?

At the very least, the corner boxes won't fall into this category. Every corner box has three painted sides.

As stated in the previous hint, all the corner pieces of the big cube have three painted sides.

Additionally, with the exception of corner boxes, all the small cubes that touch another face of the big cube have two painted sides.

As shown in the diagram, the only small cubes that have one side painted are the ones located in the dead center of each face of the big cube. Each face of the big cube has only one of these.


Solution

Incorrect

Too bad!

Think about where a cube has to be situated in the larger structure in order to only have one red side.

Correct

That's right!

If you can dissect the block in your head in the way shown above, the answer is easy enough to come by.

As you can see, the number of small cubes with one side painted red is six, one for each face of the larger block.

CV101S

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

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