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How do they do that?

How do they do that?. Assign a symbol to cards on a straight line . Each pair of cards define a unique line... ...so have a unique symbol in common! 7 parallel lines per direction. 8 directions... Can assign extra cards for intersection of parallel lines.

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How do they do that?

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  1. How do they do that?

  2. Assign a symbol to cards on a straight line. • Each pair of cards define a unique line... • ...so have a unique symbol in common! • 7 parallel lines per direction. • 8 directions... • Can assign extra cards for intersection of parallel lines. • These also need a symbol in common. 49 cards 56 symbols 57 cards 57 symbols

  3. Finite projective plane of order n=7. • n2+n+1 cards • n2+n+1 symbols • n+1 cards / symbol • n+1 symbols / card • A set of cards with a nice mathematical structure!

  4. ...almost. Not included in pack

  5. Another representation of the structure

  6. Matching symbols occur at relative positions (mod 57)0, 1, 3, 13, 32, 36, 43, 52What is special about these numbers that makes this ordering possible?

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