IR-TST 2017 Problem 9

There are $27$ cards, each has some amount of ( $1$ or $2$ or $3$ ) shapes (a circle, a square or a triangle) with some color (white, grey or black) on them. We call a triple of cards a match such that all of them have the same amount of shapes or distinct amount of shapes, have the same shape or distinct shapes and have the same color or distinct colors. For instance, three cards shown in the figure are a match be cause they have distinct amount of shapes, distinct shapes but the same color of shapes. What is the maximum number of cards that we can choose such that non of the triples make a match?

Proposed by Amin Bahjati

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