Difference between revisions of "Where to swap (y)"

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(Minor edit)
(Removed reference to "star-marked" hexes.)
 
(5 intermediate revisions by 3 users not shown)
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*the red marked hexes should not be swapped
+
* The red marked hexes should not be swapped.
*the blue marked hexes should be swapped
+
* The blue marked hexes should be swapped.
*the star marked hexes are defining the [[Y]] board.
+
  
 
=== Regular Y / Size 2===
 
=== Regular Y / Size 2===
<hex> C2 R2
+
<hexboard size="2x2"
1:SB
+
  coords="none"
2:BB
+
  edges="none"
</hex>
+
  visible="area(a2,b2,b1)"
 +
  contents="B all"
 +
  />
  
 
=== Regular Y / Size 3===
 
=== Regular Y / Size 3===
<hex> C3 R3
+
<hexboard size="3x3"
1:SSR
+
  coords="none"
2:SBB
+
  edges="none"
3:RBR
+
  visible="area(a3,c3,c1)"
</hex>
+
  contents="R all B b2 b3 c2"
 +
  />
  
 
=== Regular Y / Size 4===
 
=== Regular Y / Size 4===
<hex> C4 R4
+
<hexboard size="4x4"
1:SSSR
+
  coords="none"
2:SSBB
+
  edges="none"
3:SBBB
+
  visible="area(a4,d4,d1)"
4:RBBR
+
  contents="B all R a4 d4 d1"
</hex>
+
  />
  
 
=== Regular Y / Size 5===
 
=== Regular Y / Size 5===
<hex> C5 R5
+
<hexboard size="5x5"
1:SSSSR
+
  coords="none"
2:SSSRR
+
  edges="none"
3:SSRBR
+
  visible="area(a5,e5,e1)"
4:SRBBR
+
  contents="R all B area(d3,c4,d4)"
5:RRRRR
+
  />
</hex>
+
  
 
=== Regular Y / Size 6===
 
=== Regular Y / Size 6===
<hex> C6 R6
+
<hexboard size="6x6"
1:SSSSSR
+
  coords="none"
2:SSSSRR
+
  edges="none"
3:SSSRRR
+
  visible="area(a6,f6,f1)"
4:SSRBBR
+
  contents="R all B area(d4,d5,e4)"
5:SRRBRR
+
  />
6:RRRRRR
+
</hex>
+
  
 
=== Regular Y / Size 7===
 
=== Regular Y / Size 7===
<hex> C7 R7
+
<hexboard size="7x7"
1:SSSSSSR
+
  coords="none"
2:SSSSSRR
+
  edges="none"
3:SSSSRBR
+
  visible="area(a7,g7,g1)"
4:SSSRBBR
+
  contents="R all B area(c6,f6,f3)"
5:SSRBBBR
+
  />
6:SRBBBBR
+
7:RRRRRRR
+
</hex>
+
  
 
=== Regular Y / Size 8===
 
=== Regular Y / Size 8===
<hex> C8 R8
+
<hexboard size="8x8"
1:SSSSSSSR
+
  coords="none"
2:SSSSSSRR
+
  edges="none"
3:SSSSSRRR
+
  visible="area(a8,h8,h1)"
4:SSSSRBBR
+
  contents="R all B f4--f7,g4--d7,d6--g6"
5:SSSRRBRR
+
  />
6:SSRBBBBR
+
7:SRRBRBRR
+
8:RRRRRRRR
+
</hex>
+
  
 
=== Regular Y / Size 9===
 
=== Regular Y / Size 9===
<hex> C9 R9
+
<hexboard size="9x9"
1:SSSSSSSSR
+
  coords="none"
2:SSSSSSSRR
+
  edges="none"
3:SSSSSSRRR
+
  visible="area(a9,i9,i1)"
4:SSSSSRRRR
+
  contents="R all B area(g5,g7,e7)"
5:SSSS_RBR_
+
  />
6:SSSRRBBRR
+
7:SSRRBBBRR
+
8:SRRRRRRRR
+
9:RRRR_RRRR
+
</hex>
+
 
+
<hex> C9 R9
+
1:SSSSSSSS_
+
2:SSSSSSS__
+
3:SSSSSS___
+
4:SSSSS____
+
5:SSSS__P__
+
6:SSS__PP__
+
7:SS__PPP__
+
8:S________
+
9:____B____
+
</hex>
+
Up to symmetry, the only move with unknown status is the middle cell along an edge. So suppose Blue plays first here. By a strategy stealing argument, Red can not hope to win by responding with another middle edge move. This leaves only the six marked cells to be investigated.
+
 
+
 
+
<hex> C9 R9
+
1:SSSSSSSS_
+
2:SSSSSSS__
+
3:SSSSSS___
+
4:SSSSS____
+
5:SSSS__R__
+
6:SSS______
+
7:SS___B___
+
8:S________
+
9:____B____
+
</hex>
+
If Red plays here, Blue wins easily with this continuation.
+
 
+
 
+
<hex> C9 R9
+
1:SSSSSSSS_
+
2:SSSSSSS__
+
3:SSSSSS___
+
4:SSSSS____
+
5:SSSS_____
+
6:SSS______
+
7:SS___BR__
+
8:S________
+
9:____B____
+
</hex>
+
This red move is somewhat better, but Blue can win with the same response.
+
 
+
 
+
<hex> C9 R9
+
1:SSSSSSSS_
+
2:SSSSSSS__
+
3:SSSSSS___
+
4:SSSSS____
+
5:SSSS__B__
+
6:SSS______
+
7:SS___R___
+
8:S________
+
9:____B____
+
</hex>
+
And if Red plays here himself, Blue can win as shown.
+
 
+
 
+
<hex> C9 R9
+
1:SSSSSSSSP
+
2:SSSSSSS__
+
3:SSSSSS___
+
4:SSSSS____
+
5:SSSS_____
+
6:SSSPP_R__
+
7:SSPP_____
+
8:SPPPP____
+
9:PPPPB___P
+
</hex>
+
Red essentially only has one option left. This move seems promising, since it wins if Blue had played any of the marked cells instead as his first move.
+
 
+
 
+
<hex> C9 R9
+
1:SSSSSSSS_
+
2:SSSSSSS__
+
3:SSSSSS___
+
4:SSSSS____
+
5:SSSS_____
+
6:SSS___R__
+
7:SS__P_P__
+
8:S________
+
9:____B____
+
</hex>
+
However, it is currently unknown who wins if Blue plays either of the two marked cells next, as they can lead to rather complicated positions. All others are losing for Blue.
+
 
+
  
 
=== Regular Y / Size 10===
 
=== Regular Y / Size 10===
<hex> C10 R10
+
<hexboard size="10x10"
1:SSSSSSSSSR
+
  coords="none"
2:SSSSSSSS__
+
  edges="none"
3:SSSSSSS___
+
  visible="area(a10,j10,j1)"
4:SSSSSS____
+
  contents="R all E area(e5,e11,k5) B area(f7,f8,g8,h7,h6,g6)"
5:SSSSS_____
+
  />
6:SSSS______
+
7:SSS___B___
+
8:SS________
+
9:S_________
+
10:R________R
+
</hex>
+
  
 
=== Regular Y / Bent-27===
 
=== Regular Y / Bent-27===
Line 190: Line 87:
  
 
=== Master Y / Size 2===
 
=== Master Y / Size 2===
<hex> C2 R2
+
<hexboard size="2x2"
1:SR
+
  coords="none"
2:RR
+
  edges="none"
</hex>
+
  visible="area(a2,b2,b1)"
 +
  contents="R all"
 +
  />
  
 
=== Master Y / Size 3===
 
=== Master Y / Size 3===
<hex> C3 R3
+
<hexboard size="3x3"
1:SSR
+
  coords="none"
2:SBB
+
  edges="none"
3:RBR
+
  visible="area(a3,c3,c1)"
</hex>
+
  contents="R all B area(b3,c2,b2)"
 +
  />
  
 
=== Master Y / Size 4===
 
=== Master Y / Size 4===
<hex> C4 R4
+
<hexboard size="4x4"
1:SSSR
+
  coords="none"
2:SSRR
+
  edges="none"
3:SRBR
+
  visible="area(a4,d4,d1)"
4:RRRR
+
  contents="R all B c3"
</hex>
+
  />
  
 
=== Master Y / Size 5===
 
=== Master Y / Size 5===
<hex> C5 R5
+
<hexboard size="5x5"
1:SSSSR
+
  coords="none"
2:SSSRR
+
  edges="none"
3:SSRRR
+
  visible="area(a5,e5,e1)"
4:SRRRR
+
  contents="R all"
5:RRRRR
+
  />
</hex>
+
  
 
=== Master Y / Size 6===
 
=== Master Y / Size 6===
<hex> C6 R6
+
<hexboard size="6x6"
1:SSSSSR
+
  coords="none"
2:SSSSRR
+
  edges="none"
3:SSSRRR
+
  visible="area(a6,f6,f1)"
4:SSR__R
+
  contents="R all B area(d4,d5,e4)"
5:SRR_RR
+
  />
6:RRRRRR
+
</hex>
+
  
 
=== Master Y / Bent-27===
 
=== Master Y / Bent-27===
Line 234: Line 131:
  
 
Again, status unknown but presumably within reach for computers.
 
Again, status unknown but presumably within reach for computers.
 +
 +
== See also ==
 +
For corresponding information on Hex, please visit [[Small boards]].
  
 
[[category:Y]]
 
[[category:Y]]

Latest revision as of 01:42, 19 January 2021

  • The red marked hexes should not be swapped.
  • The blue marked hexes should be swapped.

Regular Y / Size 2

Regular Y / Size 3

Regular Y / Size 4

Regular Y / Size 5

Regular Y / Size 6

Regular Y / Size 7

Regular Y / Size 8

Regular Y / Size 9

Regular Y / Size 10

Regular Y / Bent-27

Y27 bent.gif

This board (on which the pieces are placed on the intersections) should be within reach for computers, but no results are known so far.

Master Y

In Master Y, the first player places one piece on the board, and each subsequent move consists of placing two pieces on the board.

  • the red marked hexes are losing first moves
  • the blue marked hexes are winning first moves

Master Y / Size 2

Master Y / Size 3

Master Y / Size 4

Master Y / Size 5

Master Y / Size 6

Master Y / Bent-27

Y27 bent.gif

Again, status unknown but presumably within reach for computers.

See also

For corresponding information on Hex, please visit Small boards.