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

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(Updated and edited Regular Size 9 - middle edge cell opening)
(flip red/blue convention, for consistency with hex pages)
 
(11 intermediate revisions by 4 users not shown)
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*the red marked hexes should not be swapped
+
* The red marked hexes should be swapped.
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*the blue marked hexes should be swapped
+
* The blue marked hexes should not be swapped.
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*the star marked hexes are defining the [[Y]] board.
+
  
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=== Regular Y / Size 2===
+
== Regular Y ==
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<hex> C2 R2
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−
1:SB
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−
2:BB
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−
</hex>
+
  
−
=== Regular Y / Size 3===
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=== Size 2 ===
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<hex> C3 R3
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<hexboard size="2x2"
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1:SSR
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  coords="none"
−
2:SBB
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  edges="none"
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3:RBR
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  visible="area(a2,b2,b1)"
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</hex>
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  contents="S red:all"
 +
  />
  
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=== Regular Y / Size 4===
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=== Size 3 ===
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<hex> C4 R4
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<hexboard size="3x3"
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1:SSSR
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  coords="none"
−
2:SSBB
+
  edges="none"
−
3:SBBB
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  visible="area(a3,c3,c1)"
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4:RBBR
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  contents="S blue:all red:(b2 b3 c2)"
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</hex>
+
  />
  
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=== Regular Y / Size 5===
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=== Size 4 ===
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<hex> C5 R5
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<hexboard size="4x4"
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1:SSSSR
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  coords="none"
−
2:SSSRR
+
  edges="none"
−
3:SSRBR
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  visible="area(a4,d4,d1)"
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4:SRBBR
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  contents="S red:all blue:(a4 d4 d1)"
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5:RRRRR
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  />
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</hex>
+
  
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=== Regular Y / Size 6===
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=== Size 5 ===
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<hex> C6 R6
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<hexboard size="5x5"
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1:SSSSSR
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  coords="none"
−
2:SSSSRR
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  edges="none"
−
3:SSSRRR
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  visible="area(a5,e5,e1)"
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4:SSRBBR
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  contents="S blue:all red:area(d3,c4,d4)"
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5:SRRBRR
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  />
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6:RRRRRR
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−
</hex>
+
  
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=== Regular Y / Size 7===
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=== Size 6 ===
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<hex> C7 R7
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<hexboard size="6x6"
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1:SSSSSSR
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  coords="none"
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2:SSSSSRR
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  edges="none"
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3:SSSSRBR
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  visible="area(a6,f6,f1)"
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4:SSSRBBR
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  contents="S blue:all red:area(d4,d5,e4)"
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5:SSRBBBR
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  />
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6:SRBBBBR
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7:RRRRRRR
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−
</hex>
+
  
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=== Regular Y / Size 8===
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=== Size 7 ===
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<hex> C8 R8
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<hexboard size="7x7"
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1:SSSSSSSR
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  coords="none"
−
2:SSSSSSRR
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  edges="none"
−
3:SSSSSRRR
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  visible="area(a7,g7,g1)"
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4:SSSSRBBR
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  contents="S blue:all red:area(c6,f6,f3)"
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5:SSSRRBRR
+
  />
−
6:SSRBBBBR
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−
7:SRRBRBRR
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−
8:RRRRRRRR
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−
</hex>
+
  
−
=== Regular Y / Size 9===
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=== Size 8 ===
−
<hex> C9 R9
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<hexboard size="8x8"
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1:SSSSSSSSR
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  coords="none"
−
2:SSSSSSSRR
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  edges="none"
−
3:SSSSSSRRR
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  visible="area(a8,h8,h1)"
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4:SSSSSRRRR
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  contents="S blue:all red:(f4--f7,g4--d7,d6--g6)"
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5:SSSS_RBR_
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  />
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6:SSSRRBBRR
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−
7:SSRRBBBRR
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8:SRRRRRRRR
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9:RRRR_RRRR
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−
</hex>
+
  
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<hex> C9 R9
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=== Size 9 ===
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1:SSSSSSSS_
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<hexboard size="9x9"
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2:SSSSSSS__
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  coords="none"
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3:SSSSSS___
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  edges="none"
−
4:SSSSS____
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  visible="area(a9,i9,i1)"
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5:SSSS__P__
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  contents="S blue:all red:area(g5,g7,e7)"
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6:SSS__PP__
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  />
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7:SS__PPP__
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−
8:S________
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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.
+
  
 +
=== Size 10 ===
 +
<hexboard size="10x10"
 +
  coords="none"
 +
  edges="none"
 +
  visible="area(a10,j10,j1)"
 +
  contents="S blue:all none:area(e5,e11,k5) red:area(f7,f8,g8,h7,h6,g6)"
 +
  />
  
−
<hex> C9 R9
+
=== Bent-27 ===
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1:SSSSSSSS_
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−
2:SSSSSSS__
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3:SSSSSS___
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4:SSSSS____
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5:SSSS__P__
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6:SSS______
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7:SS___P___
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8:S________
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9:____B____
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</hex>
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−
If Red plays one of these two marked cells, Blue can win by responding with the other one (!).
+
−
 
+
−
 
+
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<hex> C9 R9
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−
1:SSSSSSSS_
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2:SSSSSSS__
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3:SSSSSS___
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4:SSSSS____
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5:SSSS_____
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6:SSSPP_R__
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−
7:SSPP_____
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8:SPPPP____
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9:PPPPB____
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</hex>
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−
Red might like to try this move. It is a natural choice, since it wins if Blue had played any of the marked cells instead as his first move.
+
−
 
+
−
 
+
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<hex> C9 R9
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−
1:SSSSSSSS_
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2:SSSSSSS__
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3:SSSSSS___
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4:SSSSS____
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5:SSSS_____
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6:SSS___R__
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7:SS__P_P__
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8:S________
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9:____B____
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</hex>
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−
However, it is currently unknown who wins if Blue plays either of the two marked cells next. All others are losing for Blue.
+
−
 
+
−
 
+
−
<hex> C9 R9
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−
1:SSSSSSSS_
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2:SSSSSSS__
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3:SSSSSS___
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4:SSSSS____
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5:SSSS_____
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6:SSS______
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7:SS____R__
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8:S________
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9:____B____
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</hex>
+
−
If Blue in fact has a winning move in the previous position, Red essentially only has one option left. In this case, it seems to be more difficult to narrow down Blue's follow-ups.
+
−
 
+
−
 
+
−
=== Regular Y / Size 10===
+
−
<hex> C10 R10
+
−
1:SSSSSSSSSR
+
−
2:SSSSSSSS__
+
−
3:SSSSSSS___
+
−
4:SSSSSS____
+
−
5:SSSSS_____
+
−
6:SSSS______
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7:SSS___B___
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−
8:SS________
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9:S_________
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10:R________R
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</hex>
+
−
 
+
−
=== Regular Y / Bent-27===
+
  
 
[[Image:Y27_bent.gif]]
 
[[Image:Y27_bent.gif]]
Line 169: Line 82:
 
This board (on which the pieces are placed on the intersections) should be within reach for computers, but no results are known so far.
 
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===
+
== 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.
 
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 red marked hexes are winning first moves
−
*the blue marked hexes are winning first moves
+
*the blue marked hexes are losing first moves
  
−
=== Master Y / Size 2===
+
=== Size 2 ===
−
<hex> C2 R2
+
<hexboard size="2x2"
−
1:SR
+
  coords="none"
−
2:RR
+
  edges="none"
−
</hex>
+
  visible="area(a2,b2,b1)"
 +
  contents="S blue:all"
 +
  />
  
−
=== Master Y / Size 3===
+
=== 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="S blue:all red:area(b3,c2,b2)"
 +
  />
  
−
=== Master Y / Size 4===
+
=== 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="S blue:all red:c3"
−
</hex>
+
  />
  
−
=== Master Y / Size 5===
+
=== 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="S blue:all"
−
5:RRRRR
+
  />
−
</hex>
+
  
−
=== Master Y / Size 6===
+
=== 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="S blue:all red:area(d4,d5,e4)"
−
5:SRR_RR
+
  />
−
6:RRRRRR
+
−
</hex>
+
  
−
=== Master Y / Bent-27===
+
=== Bent-27 ===
  
 
[[Image:Y27_bent.gif]]
 
[[Image:Y27_bent.gif]]
  
 
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 02:47, 21 June 2026

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

Regular Y

Size 2

Size 3

Size 4

Size 5

Size 6

Size 7

Size 8

Size 9

Size 10

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

Size 2

Size 3

Size 4

Size 5

Size 6

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.

Retrieved from "https://www.hexwiki.net/index.php?title=Where_to_swap_(y)&oldid=8970"