Dobble http://images.math.cnrs.fr/Dobble-et-la-geometrie-finie.html
projective finite plane based on ℤ₇
one point per card, one line per symbol, two points per line, 7+1
lines per point
cards: 7² (point pairs) + 7 (parallel lines) + 1 (extra parallel, the
"vertical" one) (???)
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let's try ℤ₃p
(0,0) (1,0) (2,0) | (i,0)
(0,1) (1,1) (2,1) | (i,1)
(0,2) (1,2) (2,2) | (i,2)
------------------+
(0,i)
[a] x=0 (0,0) (0,1) (0,2) (0,i)
[b] x=1 (1,0) (1,1) (1,2) (0,i)
[c] x=2 (2,0) (2,1) (2,2) (0,i)
[d] y=0 (0,0) (1,0) (2,0) (i,0)
[e] y=1 (0,1) (1,1) (2,1) (i,0)
[f] y=2 (0,2) (1,2) (2,2) (i,0)
[g] x+y=0 (0,0) (1,2) (2,1) (i,1)
[h] x+y=1 (0,1) (1,0) (2,2) (i,1)
[i] x+y=2 (0,2) (1,1) (2,0) (i,1)
[j] x+2y=0 (0,0) (1,1) (2,2) (i,2)
[k] x+2y=1 (0,2) (1,0) (2,1) (i,2)
[l] x+2y=2 (0,1) (1,2) (2,0) (i,2)
[m] x+y=i (i,0) (i,1) (i,2) (0,i)
13 lines=symbols, 13 point=cards
card symbols
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(0,0) a d g j
(0,1) a e h l
(0,2) a f i k
(0,i) abc m
(1,0) b d h k
(1,1) b e ij
(1,2) b fg l
(2,0) cd i l
(2,1) c e g k
(2,2) c f h j
(i,0) def m
(i,1) ghi m
(i,2) jklm
in "my" order:
(i,2) jklm
(i,1) hgi m
(i,0) efd m
(0,i) abc m
(2,0) c d i l
(1,2) b f g l
(0,1) a e h l
(2,1) ce g k
(1,0) b dh k
(0,2) a f i k
(2,2) c f h j
(1,1) b e ij
(0,0) a d g j