Possible examples: After staring at the definition of a set factorization for a minute, it clicked for me when I thought about Quarto.
Quarto is a simple board game played with 16 pieces (and a 4x4 grid) where each piece is (short or tall) and (light or dark) and (round or square) and (solid or hollow). There’s exactly one piece with each combination of attributes; for example, there’s exactly one tall dark round hollow piece.
Thus, the full set of 16 pieces can be factored into {{short, tall}, {light, dark}, {round, square}, {solid, hollow}}. Similarly, given that list of attributes, you can reconstruct the full set of 16 distinct pieces.
Though I think Set is a better-known game. It has 81 cards, where each card has (one, two, or three) pictures of a (diamond, oval, or squiggle) with (solid, striped, or no) shading drawn in (red, green, or purple) ink.
Possible examples: After staring at the definition of a set factorization for a minute, it clicked for me when I thought about Quarto.
Quarto is a simple board game played with 16 pieces (and a 4x4 grid) where each piece is (short or tall) and (light or dark) and (round or square) and (solid or hollow). There’s exactly one piece with each combination of attributes; for example, there’s exactly one tall dark round hollow piece.
Thus, the full set of 16 pieces can be factored into {{short, tall}, {light, dark}, {round, square}, {solid, hollow}}. Similarly, given that list of attributes, you can reconstruct the full set of 16 distinct pieces.
Though I think Set is a better-known game. It has 81 cards, where each card has (one, two, or three) pictures of a (diamond, oval, or squiggle) with (solid, striped, or no) shading drawn in (red, green, or purple) ink.
(edited for formatting)
What about Dobble / Spot-It? They are cards designed so each pair of cards has exactly one shared symbol between them.
What elements of that game are you suggesting would correspond to a set factorization? I’m not seeing one.