Question 1
A designer plans to decorate the opening ceremony for this year's IMO contest in Romania with rows of coloured clock faces. Each clock face consists of twelve coloured rectangles glued to a round white base, as illustrated below.
The following design rules apply:
1. Each rectangle is blue, yellow, or red.
2. All three colours must be used somewhere on the clock face.
Two clock faces are considered identical whenever one can be rotated to match the colours of the other.
How many distinct clock faces could be made?
The following design rules apply:
1. Each rectangle is blue, yellow, or red.
2. All three colours must be used somewhere on the clock face.
Two clock faces are considered identical whenever one can be rotated to match the colours of the other.
How many distinct clock faces could be made?