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Erik and Sanjay have these dominoes laid out:
 
dominoes 0-1, 0-2, 0-3, 1-1, 1-2, 1-3, 2-2, 2-3, 3-3

They pick a domino in turn.

Erik can only choose dominoes which have an odd number of spots in total.
Sanjay chooses the dominoes which have an even number of spots.

How many will they each be able to pick up? Is this fair? Why?

Now they change the rules. They lay out the dominoes again.

Erik can only choose dominoes where the total number of dots is a multiple of $3$.
Sanjay chooses the dominoes where the total number of dots is not a multiple of $3$.

Who is able to pick up the most dominoes now? Is this fair? Explain your answer.