HexWiki - User contributions [en]

Where to swap (y)

2020-01-09T19:33:19Z

Isometry: Completed Master Y Size 6

*the red marked hexes should not be swapped
*the blue marked hexes should be swapped
*the star marked hexes are defining the [[Y]] board.

=== Regular Y / Size 2===
<hex> C2 R2
1:SB
2:BB
</hex>

=== Regular Y / Size 3===
<hex> C3 R3
1:SSR
2:SBB
3:RBR
</hex>

=== Regular Y / Size 4===
<hex> C4 R4
1:SSSR
2:SSBB
3:SBBB
4:RBBR
</hex>

=== Regular Y / Size 5===
<hex> C5 R5
1:SSSSR
2:SSSRR
3:SSRBR
4:SRBBR
5:RRRRR
</hex>

=== Regular Y / Size 6===
<hex> C6 R6
1:SSSSSR
2:SSSSRR
3:SSSRRR
4:SSRBBR
5:SRRBRR
6:RRRRRR
</hex>

=== Regular Y / Size 7===
<hex> C7 R7
1:SSSSSSR
2:SSSSSRR
3:SSSSRBR
4:SSSRBBR
5:SSRBBBR
6:SRBBBBR
7:RRRRRRR
</hex>

=== Regular Y / Size 8===
<hex> C8 R8
1:SSSSSSSR
2:SSSSSSRR
3:SSSSSRRR
4:SSSSRBBR
5:SSSRRBRR
6:SSRBBBBR
7:SRRBRBRR
8:RRRRRRRR
</hex>

=== Regular Y / Size 9===
<hex> C9 R9
1:SSSSSSSSR
2:SSSSSSSRR
3:SSSSSSRRR
4:SSSSSRRRR
5:SSSSRRBRR
6:SSSRRBBRR
7:SSRRBBBRR
8:SRRRRRRRR
9:RRRRRRRRR
</hex>

=== Regular Y / Size 10===
<hex> C10 R10
1:SSSSSSSSSR
2:SSSSSSSSRR
3:SSSSSSSRRR
4:SSSSSSRRRR
5:SSSSS_____
6:SSSS__BB__
7:SSSR_BBB_R
8:SSRR_BB_RR
9:SRRR___RRR
10:RRRR__RRRR
</hex>

=== Regular Y / Bent-27===

[[Image: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===
<hex> C2 R2
1:SR
2:RR
</hex>

=== Master Y / Size 3===
<hex> C3 R3
1:SSR
2:SBB
3:RBR
</hex>

=== Master Y / Size 4===
<hex> C4 R4
1:SSSR
2:SSRR
3:SRBR
4:RRRR
</hex>

=== Master Y / Size 5===
<hex> C5 R5
1:SSSSR
2:SSSRR
3:SSRRR
4:SRRRR
5:RRRRR
</hex>

=== Master Y / Size 6===
<hex> C6 R6
1:SSSSSR
2:SSSSRR
3:SSSRRR
4:SSRBBR
5:SRRBRR
6:RRRRRR
</hex>

=== Master Y / Bent-27===

[[Image:Y27_bent.gif]]

Again, status unknown but presumably within reach for computers.

== See also ==
For corresponding information on Hex, please visit [[Small boards]].

[[category:Y]]

Small boards

2016-10-20T11:25:57Z

Isometry:

Playing [[Hex]] on [[board]]s of size smaller than 10 × 10 is not very interesting, since many players will be able to play almost perfectly. However it may still be intersting for theoretical studies, and for making [[Puzzles|problems]].

The boards of size up to five can be solved by hand. Hex on 6 × 6 has been solved by [[Queenbee]].

Here are the winning first moves on the small boards. [[Red (player)|Red]] is vertical and plays first. The [[Hex (board element)|cells]] containing a red [[Piece|stone]] are winning moves for red, while those containing a blue stone are losing. For more details, visit Queenbee's own [http://www.cs.ualberta.ca/~queenbee/openings.html opening page].

''Update:'' The 7 × 7 board has been solved by [[Ryan Hayward|R. Hayward]], et.al. For more details, visit http://www.cs.ualberta.ca/~hayward/hex7trees/

== Winner depending on the first move ==
The following boards can help you decide where you should [[swap]] when playing on small boards, and it might give you ideas of patterns for bigger boards.
<hex>R2 C2 Q1 Vb1 Va2 Ha1 Hb2</hex>

<hex>R3 C3 Q1 Va2 Va3 Hb1 Vb2 Hb3 Vc1 Vc2 Ha1 Hc3</hex>

<hex>R4 C4 Q1 Va4 Vb3 Vc2 Vd1 Ha1 Ha2 Ha3 Hb1 Hb2 Hb4 Hc1 Hc3 Hc4 Hd2 Hd3 Hd4</hex>

<hex>R5 C5 Q1 Ve1 Vb2 Vc2 Vd2 Ve2 Vb3 Vc3 Vd3 Va4 Vb4 Vc4 Vd4 Va5 Ha1 Ha2 Ha3 Hb1 Hc1 Hd1 Hb5 Hc5 Hd5 He5 He4 He3</hex>

<hex>R6 C6 Q1 Ve1 Vb2 Vc2 Vd2 Ve2 Vb3 Vc3 Vd3 Va4 Vb4 Vc4 Vd4 Va5 Ha1 Ha2 Va3 Hb1 Hc1 Hd1 He1 Vb5 Vc5 Vd5 Ve5 Ve4 Ve3 Vf1 Vf2 Vf3 Vf4 Hf5 Hf6 He6 Hd6 Hc6 Hb6 Va6</hex>

=== Size 7 ===

Size 7 was first solved by [[Ryan Hayward]] using [[domination]].

<hex>R7 C7 Q1 Ha1 Hb1 Hc1 Hd1 He1 Hf1 Vg1 Ha2 Hb2 Vc2 Hd2 Ve2 Vf2 Vg2 Ha3 Vb3 Vc3 Vd3 Ve3 Vf3 Hg3 Va4 Vb4 Vc4 Vd4 Ve4 Vf4 Vg4 Ha5 Vb5 Vc5 Vd5 Ve5 Vf5 Hg5 Va6 Vb6 Vc6 Hd6 Ve6 Hf6 Hg6 Va7 Hb7 Hc7 Hd7 He7 Hf7 Hg7</hex>

=== Size 8 ===

The outcomes for size 8 were computer generated by [[Javerberg]]. The solution was independently computer generated by Hayward et al. and appeared in [[INJCAI|IJCAI09]].

<hex>
R8 C8 Q1
Ha1 Hb1 Hc1 Hd1 He1 Hf1 Hg1 Vh1
Ha2 Hb2 Hc2 Hd2 He2 Hf2 Vg2 Vh2
Ha3 Vb3 Vc3 Vd3 Ve3 Vf3 Vg3 Hh3
Ha4 Vb4 Vc4 Vd4 Ve4 Vf4 Vg4 Vh4
Va5 Vb5 Vc5 Vd5 Ve5 Vf5 Vg5 Hh5
Ha6 Vb6 Vc6 Vd6 Ve6 Vf6 Vg6 Hh6
Va7 Vb7 Hc7 Hd7 He7 Hf7 Hg7 Hh7
Va8 Hb8 Hc8 Hd8 He8 Hf8 Hg8 Hh8
</hex>

=== Size 9 ===

The outcomes for size 9 are computer generated by [[University of Alberta]]'s Hex group.

<hex>
R9 C9 Q1
Ha1 Hb1 Hc1 Hd1 He1 Hf1 Hg1 Hh1 Vi1
Va2 Vb2 Vc2 Hd2 He2 Hf2 Hg2 Vh2 Vi2
Ha3 Vb3 Vc3 Vd3 Ve3 Vf3 Vg3 Vh3 Hi3
Va4 Vb4 Vc4 Vd4 Ve4 Vf4 Vg4 Vh4 Vi4
Va5 Vb5 Vc5 Vd5 Ve5 Vf5 Vg5 Vh5 Vi5
Va6 Vb6 Vc6 Vd6 Ve6 Vf6 Vg6 Vh6 Vi6
Ha7 Vb7 Vc7 Vd7 Ve7 Vf7 Vg7 Vh7 Hi7
Va8 Vb8 Hc8 Hd8 He8 Hf8 Vg8 Vh8 Vi8
Va9 Hb9 Hc9 Hd9 He9 Hf9 Hg9 Hh9 Hi9
</hex>

== Reference ==
* [[Queenbee]]'s opening [http://www.cs.ualberta.ca/~queenbee/openings.html page] is a reference for sizes under 6x6.
* This [http://www.ru.is/faculty/yngvi/pdf/HaywardBJKPR05.pdf article] by Ryan Hayward ''et al.'' is a reference for 7x7.
* This [[Little Golem]]'s forum [http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=338 thread] is a reference for size 8x8.
* This [https://webdocs.cs.ualberta.ca/~hayward/papers/pawlhayw.pdf article] by Jakub Pawlewicz and Ryan Hayward is a reference for size 9x9.

== See also ==

* [[Board size]]
* [[Jing Yang]] designed a [[decomposition method]] to find winning strategy in Hex. [http://www.ee.umanitoba.ca/~jingyang/index.html Home Page].
* For corresponding information on the game of Y, please visit [[Where to swap (y)]].

[[Category: Theory]]

Where to swap (y)

2016-10-20T11:24:34Z

Isometry:

*the red marked hexes should not be swapped
*the blue marked hexes should be swapped
*the star marked hexes are defining the [[Y]] board.

=== Regular Y / Size 2===
<hex> C2 R2
1:SB
2:BB
</hex>

=== Regular Y / Size 3===
<hex> C3 R3
1:SSR
2:SBB
3:RBR
</hex>

=== Regular Y / Size 4===
<hex> C4 R4
1:SSSR
2:SSBB
3:SBBB
4:RBBR
</hex>

=== Regular Y / Size 5===
<hex> C5 R5
1:SSSSR
2:SSSRR
3:SSRBR
4:SRBBR
5:RRRRR
</hex>

=== Regular Y / Size 6===
<hex> C6 R6
1:SSSSSR
2:SSSSRR
3:SSSRRR
4:SSRBBR
5:SRRBRR
6:RRRRRR
</hex>

=== Regular Y / Size 7===
<hex> C7 R7
1:SSSSSSR
2:SSSSSRR
3:SSSSRBR
4:SSSRBBR
5:SSRBBBR
6:SRBBBBR
7:RRRRRRR
</hex>

=== Regular Y / Size 8===
<hex> C8 R8
1:SSSSSSSR
2:SSSSSSRR
3:SSSSSRRR
4:SSSSRBBR
5:SSSRRBRR
6:SSRBBBBR
7:SRRBRBRR
8:RRRRRRRR
</hex>

=== Regular Y / Size 9===
<hex> C9 R9
1:SSSSSSSSR
2:SSSSSSSRR
3:SSSSSSRRR
4:SSSSSRRRR
5:SSSSRRBRR
6:SSSRRBBRR
7:SSRRBBBRR
8:SRRRRRRRR
9:RRRRRRRRR
</hex>

=== Regular Y / Size 10===
<hex> C10 R10
1:SSSSSSSSSR
2:SSSSSSSSRR
3:SSSSSSSRRR
4:SSSSSSRRRR
5:SSSSS_____
6:SSSS__BB__
7:SSSR_BBB_R
8:SSRR_BB_RR
9:SRRR___RRR
10:RRRR__RRRR
</hex>

=== Regular Y / Bent-27===

[[Image: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===
<hex> C2 R2
1:SR
2:RR
</hex>

=== Master Y / Size 3===
<hex> C3 R3
1:SSR
2:SBB
3:RBR
</hex>

=== Master Y / Size 4===
<hex> C4 R4
1:SSSR
2:SSRR
3:SRBR
4:RRRR
</hex>

=== Master Y / Size 5===
<hex> C5 R5
1:SSSSR
2:SSSRR
3:SSRRR
4:SRRRR
5:RRRRR
</hex>

=== Master Y / Size 6===
<hex> C6 R6
1:SSSSSR
2:SSSSRR
3:SSSRRR
4:SSR__R
5:SRR_RR
6:RRRRRR
</hex>

=== Master Y / Bent-27===

[[Image:Y27_bent.gif]]

Again, status unknown but presumably within reach for computers.

== See also ==
For corresponding information on Hex, please visit [[Small boards]].

[[category:Y]]

Printable Y boards

2016-09-05T13:35:15Z

Isometry:

For printable Hex boards, visit [[Printable boards]].

Here are some printable [[Y]] boards:

==Bent boards==
===Bent-27===
[[Image:Y27_bent.gif]]

===Bent-55===
[[Image:Y55_bent.gif]]

===Bent-93===
[[Image:Y93_bent.gif]]

==Straight boards==
===Size 4===
[[Image:Y04_straight.gif]]

===Size 5===
[[Image:Y05_straight.gif]]

===Size 6===
[[Image:Y06_straight.gif]]

===Size 7===
[[Image:Y07_straight.gif]]

===Size 8===
[[Image:Y08_straight.gif]]

===Size 9===
[[Image:Y09_straight.gif]]

===Size 10===
[[Image:Y10_straight.gif]]

===Size 11===
[[Image:Y11_straight.gif]]

===Size 12===
[[Image:Y12_straight.gif]]

===Size 13===
[[Image:Y13_straight.gif]]

===Size 14===
[[Image:Y14_straight.gif]]

===Size 15===
[[Image:Y15_straight.gif]]

===Size 16===
[[Image:Y16_straight.gif]]

===Size 17===
[[Image:Y17_straight.gif]]

===Size 18===
[[Image:Y18_straight.gif]]

===Size 19===
[[Image:Y19_straight.gif]]

[[Category:Y]]

Printable Y boards

2016-09-05T13:33:49Z

Isometry:

For printable Hex boards, visit [[Printable boards]].

Here are some printable [[Y]] boards:

===Bent-27===
[[Image:Y27_bent.gif]]

===Bent-55===
[[Image:Y55_bent.gif]]

===Bent-93===
[[Image:Y93_bent.gif]]

===Size 4===
[[Image:Y04_straight.gif]]

===Size 5===
[[Image:Y05_straight.gif]]

===Size 6===
[[Image:Y06_straight.gif]]

===Size 7===
[[Image:Y07_straight.gif]]

===Size 8===
[[Image:Y08_straight.gif]]

===Size 9===
[[Image:Y09_straight.gif]]

===Size 10===
[[Image:Y10_straight.gif]]

===Size 11===
[[Image:Y11_straight.gif]]

===Size 12===
[[Image:Y12_straight.gif]]

===Size 13===
[[Image:Y13_straight.gif]]

===Size 14===
[[Image:Y14_straight.gif]]

===Size 15===
[[Image:Y15_straight.gif]]

===Size 16===
[[Image:Y16_straight.gif]]

===Size 17===
[[Image:Y17_straight.gif]]

===Size 18===
[[Image:Y18_straight.gif]]

===Size 19===
[[Image:Y19_straight.gif]]

[[Category:Y]]

Printable boards

2016-09-05T13:29:31Z

Isometry:

Here are some printable Hex boards.

==Diamond orientation==

=== Size 4===
[[Image:Hex04.gif]]
[[Image:Hex04e.gif]]

===Size 5===
[[Image:Hex05.gif]]
[[Image:Hex05e.gif]]

===Size 6===
[[Image:Hex06.gif]]

[[Image:Hex06e.gif]]
===Size 7===
[[Image:Hex07.gif]]

[[Image:Hex07e.gif]]
===Size 8===
[[Image:Hex08.gif]]

[[Image:Hex08e.gif]]
===Size 9===
[[Image:Hex09.gif]]

[[Image:Hex09e.gif]]
=== Size 10 ===
[[Image:Hex10.gif]]

[[Image:Hex10e.gif]]
===Size 11===
[[Image:Hex11.gif]]

[[Image:Hex11e.gif]]
===Size 12===
[[Image:Hex12.gif]]

[[Image:Hex12e.gif]]
===Size 13===
[[Image:Hex13.gif]]

[[Image:Hex13e.gif]]
===Size 14===
[[Image:Hex14.gif]]

[[Image:Hex14e.gif]]
===Size 15===
[[Image:Hex15.gif]]

[[Image:Hex15e.png]]
===Size 16===
[[Image:Hex16.gif]]

[[Image:Hex16e.png]]
===Size 17===
[[Image:Hex17.gif]]

[[Image:Hex17e.png]]
===Size 18===
[[Image:Hex18.gif]]

[[Image:Hex18e.png]]
===Size 19===
[[Image:Hex19.gif]]

[[Image:Hex19e.png]]
== Bent Hex ==
[[Image:hex_bent4_lines.gif]]

==Horizontal/vertical orientation==

===Size 4===
[[Image:Hex04h.gif]]

===Size 5===
[[Image:Hex05h.gif]]

===Size 6===
[[Image:Hex06h.gif]]

===Size 7===
[[Image:Hex07h.gif]]

===Size 8===
[[Image:Hex08h.gif]]

===Size 9===
[[Image:Hex09h.gif]]

===Size 10===
[[Image:Hex10h.gif]]

===Size 11===
[[Image:Hex11h.gif]]

===Size 12===
[[Image:Hex12h.gif]]

===Size 13===
[[Image:Hex13h.gif]]

===Size 14===
[[Image:Hex14h.gif]]

===Size 15===
[[Image:Hex15h.gif]]

===Size 16===
[[Image:Hex16h.gif]]

===Size 17===
[[Image:Hex17h.gif]]

===Size 18===
[[Image:Hex18h.gif]]

===Size 19===
[[Image:Hex19h.gif]]

==Four per Sheet==

Four 11x11 hex boards on an American 8.5"-11" sheet of paper. Ideal for printing and playing with colored pencils or markers.

[[Image:4xHex11.gif]]

==EPS full color any size==

Using [[User:Tom239|Tom Ace]]'s [http://www.minortriad.com/golem2eps.html golem2eps] using as input a [[Smart Game Format|SGF]] file of a blank [[Hex]] game you can get a superb board of any size desired in EPS (as vector graphics).

For example: using just "SZ[12]" will produce a 12x12 board.

== See also ==
*[[Printable Y boards]]
*[http://commons.wikimedia.org/wiki/Image:Hex_board_11x11.svg Wikimedia Commons: 11x11 Hex board as vector graphics]

File:Hex19h.gif

2016-09-05T13:25:48Z

Isometry:

File:Hex18h.gif

2016-09-05T13:25:15Z

Isometry:

File:Hex17h.gif

2016-09-05T13:24:37Z

Isometry:

File:Hex19.gif

2016-09-05T13:24:04Z

Isometry:

File:Hex18.gif

2016-09-05T13:23:41Z

Isometry:

File:Hex17.gif

2016-09-05T13:23:20Z

Isometry:

File:Hex19e.png

2016-09-05T13:22:56Z

Isometry:

File:Hex18e.png

2016-09-05T13:22:36Z

Isometry:

File:Hex17e.png

2016-09-05T13:22:15Z

Isometry:

File:Hex16e.png

2016-09-05T13:21:51Z

Isometry:

File:Hex15e.png

2016-09-05T13:21:17Z

Isometry:

Talk:Printable boards

2016-09-05T09:07:16Z

Isometry:

I've just added boards with horizontal/vertical orientation, using the hex commands. But that doesn't make nice .gif files like the diamond shaped ones. If someone can make .gif's of horizontal/vertical boards, that would be great. [[User:Artduval|Artduval]] 04:29, 3 May 2008 (CEST)

Fixed. [[User:Isometry|Isometry]] 5 September 2016

Printable boards

2016-09-05T09:05:44Z

Isometry:

Here are some printable Hex boards.

==Diamond orientation==

=== Size 4===
[[Image:Hex04.gif]]
[[Image:Hex04e.gif]]

===Size 5===
[[Image:Hex05.gif]]
[[Image:Hex05e.gif]]

===Size 6===
[[Image:Hex06.gif]]

[[Image:Hex06e.gif]]
===Size 7===
[[Image:Hex07.gif]]

[[Image:Hex07e.gif]]
===Size 8===
[[Image:Hex08.gif]]

[[Image:Hex08e.gif]]
===Size 9===
[[Image:Hex09.gif]]

[[Image:Hex09e.gif]]
=== Size 10 ===
[[Image:Hex10.gif]]

[[Image:Hex10e.gif]]
===Size 11===
[[Image:Hex11.gif]]

[[Image:Hex11e.gif]]
===Size 12===
[[Image:Hex12.gif]]

[[Image:Hex12e.gif]]
===Size 13===
[[Image:Hex13.gif]]

[[Image:Hex13e.gif]]
===Size 14===
[[Image:Hex14.gif]]

[[Image:Hex14e.gif]]
===Size 15===
[[Image:Hex15.gif]]

[[Image:Hex15e.gif]]
===Size 16===
[[Image:Hex16.gif]]

[[Image:Hex16e.gif]]
== Bent Hex ==
[[Image:hex_bent4_lines.gif]]

==Horizontal/vertical orientation==

===Size 4===
[[Image:Hex04h.gif]]

===Size 5===
[[Image:Hex05h.gif]]

===Size 6===
[[Image:Hex06h.gif]]

===Size 7===
[[Image:Hex07h.gif]]

===Size 8===
[[Image:Hex08h.gif]]

===Size 9===
[[Image:Hex09h.gif]]

===Size 10===
[[Image:Hex10h.gif]]

===Size 11===
[[Image:Hex11h.gif]]

===Size 12===
[[Image:Hex12h.gif]]

===Size 13===
[[Image:Hex13h.gif]]

===Size 14===
[[Image:Hex14h.gif]]

===Size 15===
[[Image:Hex15h.gif]]

===Size 16===
[[Image:Hex16h.gif]]

==Four per Sheet==

Four 11x11 hex boards on an American 8.5"-11" sheet of paper. Ideal for printing and playing with colored pencils or markers.

[[Image:4xHex11.gif]]

==EPS full color any size==

Using [[User:Tom239|Tom Ace]]'s [http://www.minortriad.com/golem2eps.html golem2eps] using as input a [[Smart Game Format|SGF]] file of a blank [[Hex]] game you can get a superb board of any size desired in EPS (as vector graphics).

For example: using just "SZ[12]" will produce a 12x12 board.

== See also ==
*[[Printable Y boards]]
*[http://commons.wikimedia.org/wiki/Image:Hex_board_11x11.svg Wikimedia Commons: 11x11 Hex board as vector graphics]

File:Hex16h.gif

2016-09-05T09:01:04Z

Isometry:

File:Hex15h.gif

2016-09-05T09:00:48Z

Isometry:

File:Hex14h.gif

2016-09-05T09:00:32Z

Isometry:

File:Hex13h.gif

2016-09-05T09:00:16Z

Isometry:

File:Hex12h.gif

2016-09-05T09:00:00Z

Isometry:

File:Hex11h.gif

2016-09-05T08:59:45Z

Isometry:

File:Hex10h.gif

2016-09-05T08:59:29Z

Isometry:

File:Hex09h.gif

2016-09-05T08:59:14Z

Isometry:

File:Hex08h.gif

2016-09-05T08:58:59Z

Isometry:

File:Hex07h.gif

2016-09-05T08:58:41Z

Isometry:

File:Hex06h.gif

2016-09-05T08:58:24Z

Isometry:

File:Hex05h.gif

2016-09-05T08:58:08Z

Isometry:

File:Hex04h.gif

2016-09-05T08:57:51Z

Isometry:

Printable boards

2016-08-31T18:03:11Z

Isometry:

Here are some printable Hex boards.

==Diamond orientation==

=== Size 4===
[[Image:Hex04.gif]]
[[Image:Hex04e.gif]]

===Size 5===

[[Image:Hex05.gif]]
[[Image:Hex05e.gif]]

===Size 6===
[[Image:Hex06.gif]]

[[Image:Hex06e.gif]]
===Size 7===
[[Image:Hex07.gif]]

[[Image:Hex07e.gif]]
===Size 8===
[[Image:Hex08.gif]]

[[Image:Hex08e.gif]]
===Size 9===
[[Image:Hex09.gif]]

[[Image:Hex09e.gif]]
=== Size 10 ===
[[Image:Hex10.gif]]

[[Image:Hex10e.gif]]
===Size 11===
[[Image:Hex11.gif]]

[[Image:Hex11e.gif]]
===Size 12===
[[Image:Hex12.gif]]

[[Image:Hex12e.gif]]
===Size 13===
[[Image:Hex13.gif]]

[[Image:Hex13e.gif]]
===Size 14===
[[Image:Hex14.gif]]

[[Image:Hex14e.gif]]
===Size 15===
[[Image:Hex15.gif]]

[[Image:Hex15e.gif]]
===Size 16===
[[Image:Hex16.gif]]

[[Image:Hex16e.gif]]
== Bent Hex ==
[[Image:hex_bent4_lines.gif]]

==Horizontal/vertical orientation==

To print these, you'll need to take a picture, and you'll probably want to enlarge the picture.

===Size 4===
<hex>
R4 C4
</hex>

===Size 5===
<hex>
R5 C5
</hex>

===Size 6===
<hex>
R6 C6
</hex>

===Size 7===
<hex>
R7 C7
</hex>

===Size 8===
<hex>
R8 C8
</hex>

===Size 9===
<hex>
R9 C9
</hex>

===Size 10===
<hex>
R10 C10
</hex>

===Size 11===
<hex>
R11 C11
</hex>

===Size 12===
<hex>
R12 C12
</hex>

===Size 13===
<hex>
R13 C13
</hex>

===Size 14===
<hex>
R14 C14
</hex>

==Four per Sheet==

Four 11x11 hex boards on an American 8.5"-11" sheet of paper. Ideal for printing and playing with colored pencils or markers.

[[Image:4xHex11.gif]]

==EPS full color any size==

Using [[User:Tom239|Tom Ace]]'s [http://www.minortriad.com/golem2eps.html golem2eps] using as input a [[Smart Game Format|SGF]] file of a blank [[Hex]] game you can get a superb board of any size desired in EPS (as vector graphics).

For example: using just "SZ[12]" will produce a 12x12 board.

== See also ==
*[[Printable Y boards]]
*[http://commons.wikimedia.org/wiki/Image:Hex_board_11x11.svg Wikimedia Commons: 11x11 Hex board as vector graphics]

File:Hex16e.gif

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Isometry:

File:Hex16.gif

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Isometry:

File:Hex15e.gif

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Isometry:

File:Hex15.gif

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Isometry:

Printable Y boards

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Isometry:

For printable Hex boards, visit [[Printable boards]].

Here are some printable [[Y]] boards:

[[Image:Y27_bent.gif]]

[[Image:Y55_bent.gif]]

[[Image:Y93_bent.gif]]

[[Image:Y04_straight.gif]]

[[Image:Y05_straight.gif]]

[[Image:Y06_straight.gif]]

[[Image:Y07_straight.gif]]

[[Image:Y08_straight.gif]]

[[Image:Y09_straight.gif]]

[[Image:Y10_straight.gif]]

[[Image:Y11_straight.gif]]

[[Image:Y12_straight.gif]]

[[Image:Y13_straight.gif]]

[[Image:Y14_straight.gif]]

[[Image:Y15_straight.gif]]

[[Image:Y16_straight.gif]]

[[Image:Y17_straight.gif]]

[[Image:Y18_straight.gif]]

[[Image:Y19_straight.gif]]

[[Category:Y]]

File:Y19 straight.gif

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Isometry:

File:Y18 straight.gif

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Isometry:

File:Y17 straight.gif

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Isometry:

File:Y16 straight.gif

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Isometry:

Y

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Isometry: /* On the web */

The game of Y is a [[connection game]] invented by [[Craige Schenstead]] and [[Charles Titus]]. In its original form, it is played on a [[triangular grid of hexagons]]. There are two [[Player (general)|players]], who have one colour each, and a move consists of placing a piece of your colour in one of the hexagons on the board. The winner is the first player to complete a [[chain]] connecting all three sides of the board. Y is a kind of generalisation of [[Hex]], perhaps the one the nearest from it, but there are some strategic peculiarities, such as [[corner template]]s

[[Image:Y-board-straight.gif]]

== No draws ==

Y cannot end in a draw. That is, once the board is complete there must be one and only one winner.

=== Less than two winners ===
There cannot be two winners at the same time. If there were, each player would have a region of the board touching all three sides of the triangle as well as the opponent's region. Considering the three sides as regions themselves, this gives a map of five regions, each of which is adjacent to the other four. However, this is impossible, as the graph K5 is non-planar.

=== At least one winner ===
It can be proved by an algorithm that once a board is complete there is at least one player linking the 3 sides. Let the "state" of a board refer to the answer to the question "Is there at least one winner?" We want to prove that the state of every board is "Yes".

''First step'': if there is a pawn group (red for instance) completely surrounded by the opponent (blue for instance) let's consider the board with this pawn group replaced by opponent's pawns (blue ones). The new board has the same status as the older one as the remote group was not winning and the new big (blue) one is winning iff it was in the former board. Also note that there is still at least one group left.

Repeat this step until there is no completely surrounded group more (of either color). The board obtained has the same state as the original.

''Second step'': if there is a pawn group surrounded by the opponent and a side, removing it does not change the state of the board (for similar reasons as in step 1) and there is still at least one group left.

Repeat this step.

''Third step'': if there is a pawn group surrounded by the opponent and two sides removing it does not change the state of the board (for similar reasons as in step 1) and there is still at least one group left.

Repeat this step.

It is quite clear that after applying this algorithm there is no group connected to more than 1 opponent's groups. No group is connected to zero sides and one opponent's group, no group is connected to one side and one opponent's group, no group is connected to two sides and one opponent's group. No group can be connected to 0 1 or 2 sides without connecting an opponent group. Moreover there is at least one group left. Hence this group left is connected to 3 sides.

So the state of the board is "yes"; as it is the same as the state of the beginning board, there was a winner to begin with.

Note that this algorithm ends because the number of different groups is finite.

=== Extension to [[Hex]] ===

The proof above extends to Hex because a Hex game can be seen as a subset of a Y game.

For instance consider the following Y board of size 8. (The star marked hexes are not a part of the board.)
<hex> C8 R8
1:SSSSSSS_
2:SSSSSS__
3:SSSSS___
4:SSSS____
5:SSS_____
6:SS______
7:S_______</hex>

We can simulate a Hex game of [[size]] 4 on it.
<hex> C8 R8
1:SSSSSSSR
2:SSSSSSRR
3:SSSSSRRR
4:SSSSRRRR
5:SSSB____
6:SSBB____
7:SBBB____
8:BBBB____</hex>

Now the only way to win for Blue is to cross the board horizontally, whereas the only way for Red to do so is to cross the board verticaly.

Each game of Hex on size n Hex board can be played on a Y board of size 2n or 2n-1 with the rules of Y, player just need to play some stones to "construct" the Hex board.

== The first player wins ==
In Y the [[strategy-stealing argument]] can be applied. It proves that the second player has no winning strategy. The argument is that if the second player had a winning strategy, then the first player could chose a random first move and then pretend that she is the second player and apply the stratey. An important point is that an extra pawn is not a disadvantage in Y. Y is a complete and perfect information game in wich no draw can be conceived, so there is a winning strategy for one player. The second player has no winning strategy so the first player has one.

== Swap ==

The [[Swap rule]] can be used in Y too, the corner are bad moves to be played so there may well exist average moves to begin with. Further information on [[where to swap (y)|where to swap]].

== Variations ==

The game is usually played with the [[swap_rule]]. Alternatively, one can play Double-move Y, also known as [[Master Y]]: The first player places one piece on the board, and each subsequent move consists of placing two pieces on the board. This is a pretty challenging variant, even on small boards.

The inventors tried out a number of alternative playing grids, and eventually concluded that the most suitable one is the following "bent" version. The pieces are placed on the intersections (like in [[Go]]).

[[Image:Y93_bent.gif]]

== See also ==

You can find more boards here: [[Printable Y boards]]

Help for [[programming the bent Y board]]

Try this [[Y puzzle]].

== On the web ==

* http://www.gamepuzzles.com/gameofy.htm
* http://www.gamepuzzles.com/revugy.htm (Games magazine reviews)
* http://home.flash.net/~markthom/html/the_game_of_y.html (Dead link?)
* http://www.neutreeko.net/y.htm
* http://www.iggamecenter.com/ ('''igGameCenter''' - play "Y" online with other opponents from your iGoogle homepage)

[[Category: Y]]
[[Category: Theory]]

Where to swap (y)

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Isometry:

*the red marked hexes should not be swapped
*the blue marked hexes should be swapped
*the star marked hexes are defining the [[Y]] board.

=== Regular Y / Size 2===
<hex> C2 R2
1:SB
2:BB
</hex>

=== Regular Y / Size 3===
<hex> C3 R3
1:SSR
2:SBB
3:RBR
</hex>

=== Regular Y / Size 4===
<hex> C4 R4
1:SSSR
2:SSBB
3:SBBB
4:RBBR
</hex>

=== Regular Y / Size 5===
<hex> C5 R5
1:SSSSR
2:SSSRR
3:SSRBR
4:SRBBR
5:RRRRR
</hex>

=== Regular Y / Size 6===
<hex> C6 R6
1:SSSSSR
2:SSSSRR
3:SSSRRR
4:SSRBBR
5:SRRBRR
6:RRRRRR
</hex>

=== Regular Y / Size 7===
<hex> C7 R7
1:SSSSSSR
2:SSSSSRR
3:SSSSRBR
4:SSSRBBR
5:SSRBBBR
6:SRBBBBR
7:RRRRRRR
</hex>

=== Regular Y / Size 8===
<hex> C8 R8
1:SSSSSSSR
2:SSSSSSRR
3:SSSSSRRR
4:SSSSRBBR
5:SSSRRBRR
6:SSRBBBBR
7:SRRBRBRR
8:RRRRRRRR
</hex>

=== Regular Y / Size 9===
<hex> C9 R9
1:SSSSSSSSR
2:SSSSSSSRR
3:SSSSSSRRR
4:SSSSSRRRR
5:SSSSRRBRR
6:SSSRRBBRR
7:SSRRBBBRR
8:SRRRRRRRR
9:RRRRRRRRR
</hex>

=== Regular Y / Size 10===
<hex> C10 R10
1:SSSSSSSSSR
2:SSSSSSSSRR
3:SSSSSSSRRR
4:SSSSSSRRRR
5:SSSSS_____
6:SSSS__BB__
7:SSSR_BBB_R
8:SSRR_BB_RR
9:SRRR___RRR
10:RRRR__RRRR
</hex>

=== Regular Y / Bent-27===

[[Image: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===
<hex> C2 R2
1:SR
2:RR
</hex>

=== Master Y / Size 3===
<hex> C3 R3
1:SSR
2:SBB
3:RBR
</hex>

=== Master Y / Size 4===
<hex> C4 R4
1:SSSR
2:SSRR
3:SRBR
4:RRRR
</hex>

=== Master Y / Size 5===
<hex> C5 R5
1:SSSSR
2:SSSRR
3:SSRRR
4:SRRRR
5:RRRRR
</hex>

=== Master Y / Size 6===
<hex> C6 R6
1:SSSSSR
2:SSSSRR
3:SSSRRR
4:SSR__R
5:SRR_RR
6:RRRRRR
</hex>

=== Master Y / Bent-27===

[[Image:Y27_bent.gif]]

Again, status unknown but presumably within reach for computers.

[[category:Y]]