perplexus.info :: Games : Dice stacking

Dice stacking (Posted on 2017-11-28)

Arrange some dice, stacking them on top of each other, so that the sum of dots on each vertical side of the rectangular parallelepiped is the same.
Of course that using an even number of dice the solution is simple.
What's the smallest odd number of dice that can be used?
What's the smallest sum that can be formed?

No Solution Yet Submitted by TheKPAXian

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re: solution (spoiler)

| Comment 2 of 4 |

(In reply to solution (spoiler) by Charlie)

An easier and more general proof of impossibility for an odd number of dice:

The pips on one die add up to 21. And odd number of these dice will have an odd number of pips and therefore not be divisible by 4 as would be necessary for equal partition among the four sides of the stack.

That makes the proof valid even for non-regulation dice, where opposite faces do not necessarily add up to 7, but have randomly placed integers 1 through 6.

Posted by Charlie on 2017-11-28 10:00:11

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