MathNet 2017-part-03 — 176 problems (EN–VI) Question 117

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 mutually distinct amount of shapes, have the same shape or mutually distinct shapes and have the same color or mutually distinct colors. For instance, three cards shown in the figure are a **match** because 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
none of the triples make a **match**?