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A Stack of Dice is a puzzle in Professor Layton and the Diabolical Box.

Puzzle

You've stacked three dice in a column. At the points where the two dice touch, the faces that are touching add up to five.

If one visible face of the bottom die is showing a one, what number must be on the top face of the top die?

US Version

In case you were wondering, each die is identical, and all sets of opposing faces on each die add up to seven.

UK Version

Each die is identical and all sets of opposing faces on each die add up to seven, just like any other die.

Hints




Click a Tab to reveal the Hint.

At the two points where two dice touch, the sum of the two faces making contact equals five. If that's so, then each of these four faces must be a number between one and four.

US Version

The options for the top face of the bottom die are limited. That face can only be a two, three, or four.

UK Version

The options for the top face of the bottom die are limited. That face can only be a two, three or four.

US Version

Assume for a minute that the top face of the bottom die is a four. If so, then the bottom face of the middle die must be a one, which would make the top face of this second die a six. Now you've ruled out one possibility, as this can't be the answer.

UK Version

Assume for a minute that the top face of the bottom die is a four. If so, then the bottom face of the middle die must be a one, which would make the top face of this second die a six. Since you know that the four faces in contact with each other must be between one and four, you can rule out this possibility.


Solution

Incorrect

Too bad!

US Version

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

UK Version

Think hard about the puzzle and try again.

Correct

That's right!

Since you know that the sum of each set of opposing faces is seven, you can easily narrow down the possibilities. When a little smart thinking, as detailed above, you'll soon arrive at the answer: six.

DB113S

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

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