Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag

Mathematics-Online problems:

Solution to the problem of the (previous) week


Problem:

On a die the numbers 1 to 6 are depicted by the common symbols. Two dice are considered equal, if they can be rotated in space in such a way that corresponding faces show the same symbol in the same arrangement. Accordingly, the dice shown below are thus all different.

\includegraphics{wuerfel}


Answer:

Number of different dice, if
$ \bullet$ opposite faces add up to 7 spots
$ \bullet$ opposite faces add up to any number of spots
$ \bullet$ at least one pair of opposite faces adds up to 9 spots


Solution:

When considering the various possibilities of depicting the numbers 2, 3, and 6, it is evident that the number of differing dice increases eightfold.


[problem of the week]