Consider a 3 by 3 square coffee table with 9 tiles set as follows:
Each tile can be red (R), white (W) or blue (B). The question is, how many distinct tables are there? For example, the table
R |
W |
B |
B |
R |
W |
W |
B |
R |
is the same as the table
W |
B |
R |
B |
R |
W |
R |
W |
B |
since one can be rotated into another by means of a 90o clockwise rotation.
Although there are 39 possibilities, not counting symmetry induced by such rotations, if we want to consider rotated tables to be equivalent, then we have to ask, how many equivalence classes are there? For example, the two tables pictured above would belong to the same equivalence class. We will learn later that the number of equivalence classes of such tables is equal to: