Mixing Colours

Discrete Mathematics Level 5

We begin with three colours (i.e. red, yellow, blue). Let this set be called Generation 1, or GEN-1. We mix each pair of colours to form GEN-2, which has six colours (i.e. red, yellow, blue, orange, purple, green). Suppose this process continues while obeying three rules:

1) If two colours are selected, there is no difference in the order of mixing. (Red + Blue = Blue + Red)

2) Each colour is its own identity. (Red + Red = Red)

3) For all generations after GEN-1, no colour created in their respective generation can be mixed until the next iteration.

(Orange, Purple, Green are created in GEN-2; thus, they cannot mix until forming GEN-3)

Determine the number of colours in the set GEN-6 (after mixing).


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