The 23 monotone symmetric simple Venn diagrams for n = 7.
For all diagrams, we show an encoding we call the RG-encoding, which is
closely related to the Grünbaum encoding: the RG-encoding is obtained by
following a curve from the interior/exterior
face, numbering and recording the curves in the order that they are
encountered. Each string of the encoding is a restricted growth string,
meaning that each number is at most one greater than the values that precede
it, with the first value being 0 (except that we take the first value to be
1). For example, the four strings corresponding to the 5 ellipse example are:
w = z = 123214121432 and
x = y = 123414341214.
For most diagrams we also show 1/7 of the diagram, as laid out
on a cylinder, and an 0-1 encoding of that layout.
======= !!! Found one !!! ======= 1 {1,2} Has polar symmetry
NOTES:
- This is "Hamilton" (P2)
10000
10101
11111
11111
11010
10000
A: 1 2 3 4 5 4 3 2 1 4 2 6 2 4 1 2 5 1 3 1 5 2 1 6 5 4 5 6 1 2 1 4 3 6 5 2
D: 1 2 3 4 5 4 3 2 1 4 2 6 2 4 1 2 5 1 3 1 5 2 1 6 5 4 5 6 1 2 1 4 3 6 5 2
C: 1 2 3 4 5 6 1 6 3 2 5 2 3 6 1 2 6 4 6 2 1 6 5 1 3 1 5 6 1 4 5 2 5 4 1 6
B: 1 2 3 4 5 6 1 6 3 2 5 2 3 6 1 2 6 4 6 2 1 6 5 1 3 1 5 6 1 4 5 2 5 4 1 6
----- ---------------------------------
X
- - --------- ------------- -----
X X X
- - ----- - - ----- - - -
X X X X X
- - - - - - - - - - -
X X X X X
- - - - - ----- - - -----
X X X
- - ----- ------------- ---------
X
- -------------------------------------
======= !!! Found one !!! ======= 5 {4,5} Has polar symmetry
NOTES:
- This is "Adelaide" (P1)
10000
11010
11111
11111
01101
00100
A: 1 2 3 4 3 2 5 6 4 1 2 1 4 3 1 3 5 6 4 3 4 6 1 3 2 4 1 3 5 2 1 2 5 6 1 3
D: 1 2 3 4 3 2 5 6 4 1 2 1 4 3 1 3 5 6 4 3 4 6 1 3 2 4 1 3 5 2 1 2 5 6 1 3
C: 1 2 3 4 5 2 5 4 1 2 6 5 1 2 3 6 1 6 3 4 1 2 1 6 2 5 2 6 3 4 5 1 6 1 5 2
B: 1 2 3 4 5 2 5 4 1 2 6 5 1 2 3 6 1 6 3 4 1 2 1 6 2 5 2 6 3 4 5 1 6 1 5 2
----- ---------------------------------
X
- - - ------------- -------------
X X X
- - - - ----- - - ----- -
X X X X X
- - - - - - - - - - -
X X X X X
- ----- - - - - ----- - -
X X X
------------- - - ------------- -
X
----------------- ---------------------
======= !!! Found one !!! ======= 7 {3,6,7,8}
NOTES:
- This is the diagram discovered by Savage and Winkler in 1992. It was
never published, but is referred to in [Gr92b].
- M1.
10000
11010
11111
11111
11001
10000
A: 1 2 3 4 2 4 5 4 2 6 1 2 5 6 5 2 5 4 3 6 1 3 4 3 6 2 1 6 5 1 3 5 3 4 1 6
D: 1 2 3 4 3 2 3 5 2 6 1 6 3 5 4 5 6 4 1 6 2 1 5 3 5 6 1 5 3 4 2 4 1 4 2 6
C: 1 2 3 4 3 2 3 5 6 4 1 6 5 6 4 2 1 4 3 1 6 3 6 5 1 4 1 2 6 5 2 5 3 5 2 4
B: 1 2 3 4 5 4 2 5 1 2 6 1 4 3 4 2 1 4 3 5 6 5 1 5 6 2 1 6 3 5 3 6 3 4 6 2
----- ---------------------------------
X
- - - ------------- -------------
X X X
- - - - ----- - - ----- -
X X X X X
- - - - - - - - - - -
X X X X X
- - - - - ----- ----- - -
X X X
- - ----- --------------------- -
X
- -------------------------------------
======= !!! Found one !!! ======= 11 {11,14,24,34}
NOTES:
- This is same as the diagram of Figure 6, pg 29, of Grunbaum,
Venn Diagrams II, Geombinatorics,
2 (1992) 25-32.
- M2
100000
100101
101111
011111
011010
001000
A: 1 2 3 4 3 2 3 4 1 5 1 4 6 2 1 2 6 5 3 5 6 2 1 2 6 2 1 5 3 5 1 4 1 5 3 2
C: 1 2 3 4 5 4 3 2 1 2 3 2 1 4 5 4 1 6 1 4 5 2 1 2 5 6 5 2 5 6 1 4 1 6 3 2
B: 1 2 3 4 5 4 3 2 3 4 1 6 1 4 1 6 3 2 3 6 1 4 1 6 5 4 3 4 5 2 1 2 5 2 1 4
D: 1 2 3 4 5 4 3 6 1 6 3 6 1 4 1 6 5 4 3 4 5 6 5 4 1 2 1 4 1 2 5 6 5 2 1 4
----- -----------------------------------------
X
- - ----------------- ------------- -----
X X X
- - ------------- - - ----- - - -
X X X X X
----- - ----- - - - - - - - -
X X X X X
--------- - - - - ----- - - -----
X X X
------------- - - ------------- ---------
X
----------------- -----------------------------
======= !!! Found one !!! ======= 13 {9,13,17,40}
NOTES:
- Never appeared before?
- M3
100000
100110
101111
111011
011010
001000
A: 1 2 3 4 2 4 5 3 1 6 3 1 4 2 1 2 6 4 5 6 4 2 1 2 3 4 3 2 1 5 1 3 1 6 5 2
C: 1 2 3 4 5 3 4 2 1 2 6 4 6 2 1 5 1 6 1 3 5 2 1 2 6 4 2 4 5 6 1 3 6 1 4 2
D: 1 2 3 4 5 3 4 6 2 1 2 4 1 3 1 6 5 3 4 3 6 3 1 4 2 4 1 3 1 2 5 6 2 5 1 3
B: 1 2 3 4 5 4 2 4 1 5 6 5 1 4 1 6 3 2 6 3 1 4 1 6 4 5 3 4 5 2 6 1 6 5 1 4
----- -----------------------------------------
X
- - ----------------- ----- -------------
X X X
- - ------------- - - - - ----- -
X X X X X
- - - ----- - ----- - - - - -
X X X X X
- ----- - - - --------- - - -----
X X X
------------- - - ------------- ---------
X
----------------- -----------------------------
======= !!! Found one !!! ======= 15 {10,15,26,32}
NOTES:
- Never appeared before?
- M4.
100000
100110
101111
111011
110010
100000
A: 1 2 3 2 4 2 3 2 1 5 1 2 6 2 1 5 1 2 1 3 1 2 1 6 4 5 4 6 1 2 1 3 6 5 4 2
D: 1 2 3 4 5 4 3 2 1 2 6 2 1 2 5 2 1 3 1 2 5 2 1 6 1 4 1 6 1 2 1 4 5 3 6 2
C: 1 2 3 4 5 6 1 6 2 6 5 6 2 6 1 4 1 6 3 6 1 4 1 6 1 2 1 6 1 3 5 4 5 3 1 6
B: 1 2 3 4 5 6 1 6 4 2 3 2 4 6 1 6 5 6 1 6 3 6 1 4 1 6 3 6 1 5 1 2 1 5 1 6
----- -----------------------------------------
X
- - ----------------- ----- -------------
X X X
- - ------------- - - - - ----- -
X X X X X
- - - ----- - ----- - - - - -
X X X X X
- - - - - ------------- - - -----
X X X
- - ----- --------------------- ---------
X
- ---------------------------------------------
======= !!! Found one !!! ======= 19 {12,16,19,38}
NOTES:
- Never appeared before?
- M5.
100000
100101
110111
011111
011010
010000
A: 1 2 3 2 4 2 5 3 5 2 1 5 1 6 1 5 1 2 3 4 2 4 1 6 4 5 4 1 6 2 1 6 3 5 4 2
D: 1 2 3 4 5 4 2 3 4 1 4 6 1 3 5 3 2 3 5 3 1 5 6 5 1 4 1 6 1 3 1 4 5 6 2 3
B: 1 2 3 4 5 6 1 5 6 2 3 2 5 6 2 1 2 4 1 6 3 6 5 6 3 6 1 3 4 3 1 2 1 4 1 6
C: 1 2 3 4 5 6 1 6 3 6 5 6 4 3 4 6 1 4 1 2 1 4 1 6 3 5 6 5 1 2 5 4 5 1 2 6
----- -----------------------------------------
X
- - ----------------- ------------- -----
X X X
- - ----- --------- - ----- - - -
X X X X X
----- - - - ----- - - - - - -
X X X X X
--------- - - - - ----- - - -----
X X X
--------- - ----- ------------- ---------
X
--------- -------------------------------------
======= !!! Found one !!! ======= 22 {22,35} Has polar symmetry
NOTES:
- This is "Massey" (P3)
100000
110001
110111
111110
111000
010000
A: 1 2 3 2 4 2 5 2 4 3 1 6 1 3 1 4 1 2 1 6 2 4 5 6 4 1 4 3 2 3 5 6 3 1 5 2
D: 1 2 3 2 4 2 5 2 4 3 1 6 1 3 1 4 1 2 1 6 2 4 5 6 4 1 4 3 2 3 5 6 3 1 5 2
C: 1 2 3 4 5 2 4 1 4 6 3 6 5 2 6 1 5 3 1 3 6 3 4 3 5 3 4 6 1 2 1 6 1 4 1 3
B: 1 2 3 4 5 2 4 1 4 6 3 6 5 2 6 1 5 3 1 3 6 3 4 3 5 3 4 6 1 2 1 6 1 4 1 3
----- -----------------------------------------
X
- - - ----------------------------- -----
X X X
- - - - ------------- ----- - - -
X X X X X
- - - - - ----- - - - ----- -
X X X X X
- - - - - - - ----- -------------
X X X
----- - - ----- -------------------------
X
--------- -------------------------------------
======= !!! Found one !!! ======= 23 {23,33} Has polar symmetry
NOTES:
- This is "Victoria" (P4)
100000
110010
110111
101111
001101
000100
A: 1 2 3 4 3 2 5 4 1 2 1 4 3 2 5 4 1 6 5 2 1 2 5 4 1 6 5 6 1 2 1 6 5 4 3 2
D: 1 2 3 4 3 2 5 4 1 2 1 4 3 2 5 4 1 6 5 2 1 2 5 4 1 6 5 6 1 2 1 6 5 4 3 2
C: 1 2 3 4 5 6 1 6 5 4 5 6 3 4 1 6 1 4 5 6 3 4 1 2 3 6 1 6 3 4 1 2 3 2 1 6
B: 1 2 3 4 5 6 1 6 5 4 5 6 3 4 1 6 1 4 5 6 3 4 1 2 3 6 1 6 3 4 1 2 3 2 1 6
----- -----------------------------------------
X
- - - --------------------- -------------
X X X
- - - - ------------- - - ----- -
X X X X X
- - ----- - ----- - - - - - -
X X X X X
- ------------- - - - - ----- - -
X X X
--------------------- - - ------------- -
X
------------------------- ---------------------
======= !!! Found one !!! ======= 25 {20,25,31,39}
NOTES:
- Never appeared before?
- M6.
100000
101001
111011
011111
001101
001000
A: 1 2 3 2 4 5 2 6 1 6 5 4 3 5 3 6 1 6 2 6 1 6 5 4 5 6 1 5 1 4 1 2 1 3 2 6
B: 1 2 3 4 2 4 5 4 6 4 1 6 5 6 1 4 1 2 1 4 1 3 6 3 5 6 1 4 1 2 6 5 2 3 2 4
D: 1 2 3 4 2 5 2 6 1 2 5 6 2 6 4 6 3 6 1 3 4 3 1 6 1 2 1 6 1 5 3 5 4 3 1 6
C: 1 2 3 4 5 3 5 2 1 2 6 2 1 2 3 4 3 2 1 3 1 4 1 6 1 5 6 2 1 6 5 6 4 3 6 2
----- -----------------------------------------
X
- - --------- --------------------- -----
X X X
- - ----- - - ------------- - - -
X X X X X
----- - - - - - ----- - - - -
X X X X X
--------- ----- - - - - ----- - -
X X X
----------------- - ----- ------------- -
X
----------------- -----------------------------
======= !!! Found one !!! ======= 27 {21,27,30,36}
NOTES:
- Never appeared before?
- M7.
100000
101010
111011
110111
010101
010000
A: 1 2 3 2 4 2 5 6 1 5 6 4 3 5 3 6 3 1 3 2 1 6 5 4 5 6 5 4 1 4 2 4 1 3 2 6
D: 1 2 3 4 3 5 3 6 1 3 5 6 4 3 4 6 4 2 1 2 4 2 1 6 3 5 6 5 1 5 2 5 4 1 2 6
C: 1 2 3 4 5 2 5 3 5 1 5 6 1 3 2 4 2 3 2 4 1 4 6 4 1 5 6 3 1 6 5 6 4 6 2 3
B: 1 2 3 4 5 2 5 4 5 6 1 6 5 6 1 4 2 3 4 3 1 3 6 3 5 1 6 4 1 6 2 5 2 3 2 4
----- -----------------------------------------
X
- - --------- ------------- -------------
X X X
- - ----- - - --------- - ----- -
X X X X X
- - - - ----- - ----- - - - -
X X X X X
- ----- - --------- - - ----- - -
X X X
--------- - ------------- ------------- -
X
--------- -------------------------------------
======= !!! Found one !!! ======= 37 {18,28,29,37}
NOTES:
- Never appeared before?
- M8.
100000
101100
111110
110111
000111
000001
A: 1 2 3 4 3 5 3 2 1 5 6 5 4 6 3 2 6 1 3 4 1 4 6 5 3 4 5 2 6 2 1 2 6 5 1 4
D: 1 2 3 4 5 2 4 1 6 4 6 3 5 2 6 2 1 2 5 3 1 3 6 4 5 3 5 4 5 6 1 2 6 4 1 3
C: 1 2 3 4 5 2 4 6 3 6 1 6 3 4 1 2 1 6 5 2 5 4 5 6 1 4 3 4 2 3 5 6 3 1 5 2
B: 1 2 3 4 5 2 5 4 5 3 1 6 3 4 1 2 1 6 2 4 5 6 4 1 3 4 3 2 5 6 3 6 1 6 5 2
----- -----------------------------------------
X
- - --------- ----- ---------------------
X X X
- - ----- - - - - ----- ---------
X X X X X
- - - - ----- - - - - - -----
X X X X X
- ----- ------------- - - - - - -
X X X
----------------------------- ----- - - -
X
----------------------------------------- -----
======= !!! Found one !!! ======= 42 {41,42,46,53}
NOTES:
- Never appeared before?
- M9.
1000000
1000011
1010111
0111101
0111000
0010000
A: 1 2 3 2 4 2 5 6 1 6 2 5 2 4 3 6 3 4 1 4 3 4 6 2 1 6 5 1 5 3 5 4 5 3 1 6
D: 1 2 3 4 3 5 3 6 1 6 5 2 4 2 5 2 6 2 1 6 3 1 4 5 4 6 4 5 1 5 4 3 2 3 1 6
C: 1 2 3 4 3 5 6 2 6 5 1 5 6 5 2 3 1 2 4 1 4 6 4 5 4 6 1 2 1 3 6 3 5 3 4 2
B: 1 2 3 4 5 4 3 4 2 4 1 2 6 1 5 3 5 2 5 3 1 3 5 6 4 6 1 2 1 4 6 5 6 3 6 2
----- -------------------------------------------------
X
- - --------------------------------- ----- -----
X X X
- - ------------- ------------- - - - - -
X X X X X
----- - ----- - - ----- - ----- - - -
X X X X X
--------- - - - - - - ------------- -----
X X X
------------- - - ----- -------------------------
X
----------------- -------------------------------------
======= !!! Found one !!! ======= 47 {45,47,52,56}
NOTES:
- Never appeared before?
- M10.
1000000
1100010
1101011
0011111
0010101
0000001
A: 1 2 3 2 4 3 5 3 2 6 1 6 5 4 3 5 4 6 4 3 1 6 1 2 5 4 5 6 1 5 4 2 1 3 2 6
B: 1 2 3 4 2 5 6 4 1 6 5 6 2 4 1 4 3 5 1 5 6 3 5 6 1 4 1 2 3 6 3 5 2 3 2 4
D: 1 2 3 4 3 5 2 3 2 6 1 2 3 6 2 5 4 6 1 4 5 4 2 6 1 6 3 5 1 5 4 3 5 4 1 6
C: 1 2 3 4 5 3 4 2 4 5 1 2 1 6 3 4 3 2 1 3 4 6 1 5 6 2 1 6 5 6 4 5 3 5 6 2
----- -------------------------------------------------
X
- - - ----------------------------- -------------
X X X
- - - - ------------- --------- - ----- -
X X X X X
----- ----- - ----- - - ----- - - - -
X X X X X
----------------- - - ----- - - ----- - -
X X X
--------------------- ------------- --------- - -
X
------------------------------------------------- -----
======= !!! Found one !!! ======= 48 {44,48} Has polar symmetry
NOTES:
- This is "Manawatu" (P6)
1000000
1000101
1101101
0111011
0011010
0010000
A: 1 2 3 4 5 4 3 4 2 4 1 4 6 4 2 1 5 3 5 2 5 1 5 6 5 4 5 6 1 2 1 4 6 3 5 2
D: 1 2 3 4 5 4 3 4 2 4 1 4 6 4 2 1 5 3 5 2 5 1 5 6 5 4 5 6 1 2 1 4 6 3 5 2
C: 1 2 3 4 5 6 1 6 4 2 5 2 4 2 6 2 1 2 3 2 6 1 5 4 5 6 5 1 5 3 5 2 5 3 1 6
B: 1 2 3 4 5 6 1 6 4 2 5 2 4 2 6 2 1 2 3 2 6 1 5 4 5 6 5 1 5 3 5 2 5 3 1 6
----- -------------------------------------------------
X
- - ------------------------- ------------- -----
X X X
- - ----- ------------- - - --------- - -
X X X X X
----- - - - ----- - ----- - ----- - -
X X X X X
--------- ----- - - - --------- - - -----
X X X
----------------- - ----- ------------- ---------
X
----------------- -------------------------------------
======= !!! Found one !!! ======= 49 {49,50,51,55}
NOTES:
- Never appeared before?
- M11.
1000000
1100100
1101101
0011111
0010110
0000100
A: 1 2 3 2 4 3 5 6 5 3 2 6 1 4 3 5 4 6 1 6 4 3 1 2 5 4 5 2 1 6 1 5 4 3 2 6
D: 1 2 3 4 5 4 3 2 6 5 1 2 1 5 4 6 5 2 1 3 6 4 1 4 6 5 3 6 3 2 1 3 6 5 4 2
C: 1 2 3 4 5 6 1 5 4 5 3 4 2 6 2 4 5 6 1 3 4 2 3 6 1 6 3 4 1 5 2 3 2 5 1 6
B: 1 2 3 4 5 6 1 6 2 5 4 5 2 6 3 4 1 6 1 4 5 3 4 6 1 2 3 5 1 5 3 4 2 3 2 6
----- -------------------------------------------------
X
- - - --------------------- ---------------------
X X X
- - - - ------------- - - ------------- -
X X X X X
----- ----- - ----- - - - - ----- - -
X X X X X
----------------- - - ----- - - - - -----
X X X
--------------------- --------- - ----- ---------
X
--------------------------------- ---------------------
======= !!! Found one !!! ======= 54 {43,54} Has polar symmetry
NOTES:
- This is "Palmerston North" (P5)
1000000
1100010
1110110
1011101
0001101
0000100
A: 1 2 3 2 4 5 3 2 3 6 1 6 2 5 2 4 3 6 3 4 1 6 3 2 1 6 5 2 1 2 5 3 4 3 1 6
D: 1 2 3 2 4 5 3 2 3 6 1 6 2 5 2 4 3 6 3 4 1 6 3 2 1 6 5 2 1 2 5 3 4 3 1 6
C: 1 2 3 4 3 5 6 2 6 5 1 2 6 3 1 2 4 3 1 3 4 6 5 6 1 2 1 3 6 3 5 4 6 3 6 2
B: 1 2 3 4 3 5 6 2 6 5 1 2 6 3 1 2 4 3 1 3 4 6 5 6 1 2 1 3 6 3 5 4 6 3 6 2
----- -------------------------------------------------
X
- - - ----------------------------- -------------
X X X
- - - - ----- ------------- - - ---------
X X X X X
- - ----- - - - ----- - ----- - -----
X X X X X
- ------------- ----- - - - --------- - -
X X X
----------------------------- - - ------------- -
X
--------------------------------- ---------------------
======= !!! Found one !!! ======= 11'
NOTES:
- Never appeared before?
- M12.
100000
010110
111110
111011
001101
000100
----- -----------------------------------------
X
----- - ------------- ----- -------------
X X X
----- - - ----- - - -- - ---------
X X X X X
- - - - - - ----- - - ---------
X X X X X
- ----- ----- - ----- - ----- - -
X X X
------------------------- - ------------- -
X
------------------------- ---------------------
X: 1 2 3 2 4 2 3 5 2 1 5 6 5 1 3 5 2 1 4 3 6 4 6 5 6 4 1 6 4 3 1 6 4 5 2 3
Y: 1 2 3 4 2 3 5 3 2 3 1 2 4 6 5 1 4 5 3 5 4 6 5 1 6 2 6 1 6 4 1 6 5 2 3 4
W: 1 2 3 4 5 6 1 4 5 6 4 5 3 5 4 5 1 4 6 2 3 1 6 3 5 3 6 2 3 1 2 4 2 1 2 6
Z: 1 2 3 4 5 6 1 5 6 5 3 5 6 4 5 1 4 2 4 1 6 4 5 1 3 6 2 3 2 4 2 3 1 2 3 6
======= !!! Found one !!! ======= 12'
NOTES:
- Never appeared before?
- M13.
Y: 1 2 3 2 4 2 3 5 2 1 5 6 5 1 2 3 1 5 4 3 6 4 6 5 6 4 1 6 3 6 4 1 4 5 2 3
W: 1 2 3 4 5 3 5 2 5 3 1 5 4 5 3 1 3 2 6 4 1 6 4 6 3 6 4 2 6 1 2 5 2 1 6 4
X: 1 2 3 4 5 4 3 2 4 1 2 6 2 1 2 3 1 2 4 6 3 6 5 1 5 3 6 5 4 5 6 5 1 6 4 3
Z: 1 2 3 4 5 4 6 1 6 5 4 6 3 6 4 6 1 4 3 5 1 2 5 3 6 3 5 2 3 1 2 4 2 1 2 5
======= !!! Found one !!! ======= 13'
NOTES:
- Never appeared before?
- M14.
Z: 1 2 3 4 2 3 2 5 2 1 5 6 1 5 2 3 1 5 4 3 6 4 5 6 4 6 1 6 3 6 4 1 5 4 2 3
X: 1 2 3 4 5 3 2 5 3 5 1 5 4 5 3 1 2 3 6 4 1 6 4 3 6 4 6 2 6 1 2 5 1 2 6 4
W: 1 2 3 4 5 3 4 2 3 2 1 2 6 1 2 4 1 2 6 3 4 6 5 1 5 4 5 6 5 3 6 5 1 6 3 4
Y: 1 2 3 4 5 3 6 1 6 5 6 3 6 4 3 6 1 3 4 5 1 2 4 5 6 4 5 2 4 2 1 2 3 1 2 5
======= !!! Found one !!! ======= 20'
NOTES:
- Never appeared before?
- M15.
Y: 1 2 3 4 2 3 2 5 2 1 5 6 1 5 3 5 2 1 4 3 6 4 5 6 4 6 1 6 4 3 1 6 5 4 2 3
X: 1 2 3 4 3 2 3 5 2 3 1 2 4 6 5 1 5 4 3 5 4 6 5 6 1 6 2 1 6 4 1 6 2 5 3 4
Z: 1 2 3 4 5 6 1 3 5 6 5 3 5 4 3 5 1 3 6 2 4 1 4 6 5 4 6 2 4 2 1 2 3 1 2 6
W: 1 2 3 4 5 6 1 5 6 4 5 6 5 3 5 1 3 2 1 3 6 3 5 1 4 6 2 4 3 2 4 2 1 2 4 6
======= !!! Found one !!! ======= 21'
NOTES:
- Never appeared before?
- M16.
X: 1 2 3 2 4 2 5 2 6 1 6 5 4 2 4 6 4 2 1 2 4 5 1 3 5 6 4 5 4 3 4 1 3 2 1 5
W: 1 2 3 4 2 5 4 5 1 5 6 1 4 2 1 5 3 2 3 5 6 5 3 5 1 6 2 6 3 1 3 5 3 4 3 2
Y: 1 2 3 4 3 2 5 2 3 2 1 5 4 5 3 1 3 2 3 6 3 4 1 4 3 6 4 2 6 2 1 2 5 1 6 4
Z: 1 2 3 4 5 3 5 2 5 1 2 6 1 3 1 6 2 6 5 6 3 6 4 1 4 3 5 6 5 4 5 6 1 6 5 3
======= !!! Found one !!! ======= 26'
NOTES:
- Never appeared before?
- M17.
Y: 1 2 3 2 4 2 5 6 1 2 5 6 4 2 4 5 4 2 1 2 6 3 4 1 6 5 4 6 4 3 4 1 3 2 1 6
Z: 1 2 3 4 2 5 4 5 1 5 6 1 2 5 4 1 3 2 3 5 6 5 3 5 1 6 3 2 1 6 3 5 3 4 3 2
X: 1 2 3 4 3 5 3 6 1 6 3 5 6 4 5 4 1 4 2 1 6 4 5 1 3 6 3 4 2 4 3 4 1 2 3 6
W: 1 2 3 4 5 2 5 3 5 2 1 2 4 6 5 1 4 3 5 4 5 6 5 1 6 2 1 4 1 2 6 2 5 2 3 4