Dice Puzzles
An original set of puzzles that require a large number of dice, so raid your boxed games before you start! You can assume that you have both left and right handed dice available (ie if the values of two pairs of opposite faces are known, the other two values can be placed on the remaining two faces in either of two ways).
Email your answers to andy.brown@puzzlemanic.com, there may be a prize for the best set of solutions received! Answer key: the maximum value requested for each total plus a description of your solution!
Dice Puzzle Number 1
Arrange any number of dice in a stack so that the sum of the spots of the faces touching each die sum to the same total. Dice must be placed precisely face to face and any die not in the bottom layer must be fully supported by a die in the next lower layer. What is the maximum height of the stack for each of the possible totals from 0 to 18? If you didn't have left and right handed dice would the best answers be different?
eg some arrangements for the totals 0 to 4 with heights 1, 2, 2, 2 and 3 (which are not neccessarily the best heights) are shown. Some hidden values must be deduced by using "opposite faces sum to 7", and a "-" is used to indicate any remaining possible value:
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