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Orienting Dice Tower


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6?

 

 

The answer is six.

Consider the four numbers of each die on the side faces of the tower

taken in ccw order starting with the front.

A tower can be built for each orientation of the top die,

namely 1 2 6 5, 1 5 6 2, 1 4 6 3 and 1 3 6 4:

1 2 6 5 - 1 5 6 2 - 1 4 6 3 - 1 3 6 4 <- top die

2 3 5 4 - 2 4 5 3 - 2 1 5 6 - 2 6 5 1

3 1 4 6 - 3 6 4 1 - 3 5 4 2 - 3 2 4 5

4 5 3 2 - 4 2 3 5 - 4 6 3 1 - 4 1 3 6

5 6 2 1 - 5 1 2 6 - 5 3 2 4 - 5 4 2 3

6 4 1 3 - 6 3 1 4 - 6 2 1 5 - 6 5 1 2 <- bottom die

 

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The answer is six.

Consider the four numbers of each die on the side faces of the tower

taken in ccw order starting with the front.

A tower can be built for each orientation of the top die,

namely 1 2 6 5, 1 5 6 2, 1 4 6 3 and 1 3 6 4:

1 2 6 5 - 1 5 6 2 - 1 4 6 3 - 1 3 6 4 <- top die

2 3 5 4 - 2 4 5 3 - 2 1 5 6 - 2 6 5 1

3 1 4 6 - 3 6 4 1 - 3 5 4 2 - 3 2 4 5

4 5 3 2 - 4 2 3 5 - 4 6 3 1 - 4 1 3 6

5 6 2 1 - 5 1 2 6 - 5 3 2 4 - 5 4 2 3

6 4 1 3 - 6 3 1 4 - 6 2 1 5 - 6 5 1 2 <- bottom die

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