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A puzzle about the card game SET, played with a deck of 81 cards.

Set is a card game designed by Marsha Falco. The deck consists of $81$ cards varying in four features:

• color (red, green, purple),
• shading (empty, striped, or solid),
• shape (oval, squiggle, or rhombus),
• number of symbols (one, two, or three).

All the cards are unique. A SET occurs when three cards satisfy the following property for each of the four attributes:

• The attribute on each card is the same,
• or the attribute on each card is different

As an example for "the same", all three cards may have striped shading. As an example for "different", the three cards may have red, green, and purple color. In order for three cards to form a SET, they must satisfy this property for all four attributes.