PAINTING THE DIE.
(
Combination and Group Problems)
In how many different ways may the numbers on a single die be marked,
with the only condition that the 1 and 6, the 2 and 5, and the 3 and 4
must be on opposite sides? It is a simple enough question, and yet it
will puzzle a good many people.
Answer:
The 1 can be marked on any one of six different sides. For every side
occupied by 1 we have a selection of four sides for the 2. For every
situation of the 2 we have two places for the 3. (The 6, 5, and 4 need
not be considered, as their positions are determined by the 1, 2, and
3.) Therefore 6, 4, and 2 multiplied together make 48 different
ways--the correct answer.
