Heyawake

[from Nikoli website]

The rectangle, divided by bold lines, is called "Room". Each number indicates how many painted cells exist in its room, while no number rooms may have any number of painted cells. Paint cells under following rules:

1. White cells must not exceed two rooms in a straight line.
2. The painted cells must not be orthogonally connected.
   
3. White cells must not be (orthogonally) separated by painted cells.

Solution:

Nuruomino (aka LITS)

[from Wikipedia]

1. Shade a tetromino on each area, such that:
2. Every pair of orthogonally adjacent tetrominoes are not equal (considering rotations and reflections),
3. The shaded cells are all orthogonally contiguous and contain no 2×2 square tetrominoes as subsets.

Solution:

DIAMOND & PIVOTS (v.2)

1. On each turn, each player passes or drops a stone on an empty cell.
   There is a swap option after the first half-turn.
2. If any diamond patterns with four friendly stones are made, the player
   must choose one, choose a stone from it (the pivot), and place
   its other three stones in a line starting from the pivot.
  2.1 Every stone (of either color) that was on those destination cells
      are captured and removed from the board.
  2.2 If, after a pivot movement, another diamond shape is made,
      the player must repeat this procedure.
3. A stone may not be played to make a group of more than four stones,
   unless it thereby makes a diamond.
4. After two consecutive passes, wins the player with more
   stones (if equal, wins the 2nd)

Sample game:
abcdefghijklmnopq
    . . . . .      1.  c7 <--pied  i5
   . . . . . .     2.  d6          j4
  . . . . x x .    3.  e7          k5
 . . o x o x . .   4.  h4          m5
. . x x . x o . .  5.  l4        j6,h4-n4::
 o o x o . . . .   6.  h6     k5,k5-e5,h4-e7:
  o x . . . . .    7.  f4          l4
   . . . . . .     8.  m5          k3
    . . . . .      9.  j4          m3
abcdefghijklmnopq 10.  b6

And then...

abcdefghijklmnopq
    . . . . .      1.  c7 <--pied  i5
   . . . . . .     2.  d6          j4
  . . . . x . .    3.  e7          k5
 . . o . x . . .   4.  h4          m5
. . . . x x x x .  5.  l4        j6,h4-n4::
 x x x x . . . .   6.  h6     k5,k5-e5,h4-e7:
  o x . . . . .    7.  f4          l4
   . . . . . .     8.  m5          k3
    . . . . .      9.  j4          m3
abcdefghijklmnopq 10.  b6

10...   l2,k3-h6::,h4k5,i5-o5:,e5i6,h6-b6::

First player resigns.


Nurikabe

[from nikoli website]

1. You cannot fill the cells containing numbers.
2. A number tells the number of continuous white cells. Each area of white cells contains only one number in it and areas are separated by black cells.
3. The black cells are linked to be an orthogonally continuous wall.
4. Black cells cannot be linked to be 2x2 square or larger.

Solution:

Filomino

[from nikoli website]

1. Fill in all empty cells with numbers under the following rules:
2. The area, connected by the same numbers horizontally or vertically, is called "Block". Separate the entire board by Blocks.
3. Each Block contains as many cells as the number it contains (e.g., a Block of 6 has 6 cells).
4. Blocks of the same size must not touch each other, horizontally or vertically.

Solution:

Hitori

[from nikoli website]

1. Paint enough cell numbers such that:
   
2. No number may appear more than once in each row and each column.
3. The painted cells must not be orthogonally connected.
4. Un-painted cells must not be orthogonally separated by painted cells.

Solution:

Akari

[from nikoli website]

1. Place circles according to the following rules.
2. Circles are permitted at any white squares. Each number indicates how many circles are next to it, vertically and horizontally.
3. Each circle 'illuminates' from it to black square or outer frame in its row and column.
4. Every white square must be illuminated and every circle should not illuminate each other.
   

Solution:
It's possible to play online at http://www.puzzle-loop.com/

Hashiwokakero

[from nikoli website]

1. The number of connections is the same as the number inside the node
   
2. There can be up to two connections between two nodes
3. Connections cannot cross nodes or other connections
4. There is a continuous path connecting all nodes

Solution:
It's possible to play online at http://www.puzzle-loop.com/

Slitherlink

[from nikoli website]

1. Connect dots with vertical / horizontal line and make one loop.
2. Numbers are the hints to know how many lines can be drawn around it.
   There may be any number of lines around cells without number.
3. Lines cannot be crossed or branch off.

Solution:
It's possible to play online at http://www.puzzle-loop.com/

Masyu

[from nikoli website]

1. Make a single loop. Lines must pass through the centers of cells horizontally or vertically and never cross, branch off, or go through the same cells twice.
2. Lines must pass through all cells containing black and white circles.
3. Lines passing through a white circle cell must go straight through the cell, then make a right-angled turn in the very next cell (on at least one side of the white circle cell).
4. Lines passing through a black circle cell must make a right angled turn immediately, in the black circle cell, then go straight for the next two cells.

Solution:

Futoshiki

A new Japanese puzzle. As in Soduku, you must place all numbers from 1 to 5 in each row and column without repetition, but you must also satisfy the less than/greater than signals.

SLOW PROGRESSIVE GO 9x9

This game uses a progressive mutator in order to increase the dynamics of the original game. However, unrestricted Go drops would kill the game so two restrictions are added: (a) each stone on a drop sequence cannot belong to the same group (b) an atari stops the sequence.

Here's an example at a 9x9 board (white won 41-40). Herein it is used the slow progressive (1222344456667...)

a b c d e f g h i
. . . o x . . . . 1: c7
. . . o x . . . . 2: g3 g6
. . o o x . x x . 3: c3 e8
. . o x . . . . . 4: e2 g8
. . . o x . . . . 5: d2 d5 e7
. . . . o x x . . 6: d4 e3 e5 f7
. . o . o x . . . 7: d1 c4 e6 f9
. . . . o o x . . 8: e1 f6 g9 h3
. . . . . o x . . 9: d3 f8
a b c d e f g h i

HYDRA CHESS

Rules:

  1. Basic chess rules apply, except:
  2. When a piece makes a capture, it reduces rank and buds off
     a piece one rank lower, leaving this behind on the exit square.
     Ranks: KQRBNP-.

------------

The Hydra game is a one-person game.

You start with a rooted tree, and at any move, you may remove one
leaf, and then duplicate (later triplicate, quadruplicate etc)
the whole remaining subtree it leaves, right down to the root.
The "n" in the n-plicate goes up one on every move, starting at 2.

                    *   *                         * *   * *
                     \ /                           \|   |/
So e.g. if we     *   *   *  ...it goes             *   *   *
delete the left    \ /   /      to this one,         \  |  /
leaf from this      *   *       when n=2.             * * *
tree...              \ /                               \|/
                      R                                 R

The number of nodes increases dramatically every time, but... the theorem is, no matter what you start with, and how you choose your leaf cuttings, IT WILL ALWAYS REDUCE to the empty tree, eventually !!

In fact, you don't even have to restrict yourself to increasing the n by one every time, you can up it in squares or powers of two or anything you like!

And it's one of those things that can be easily stated in basic number theory, (PA), but not proved there.  To prove it requires knowing about infinite ordinal numbers up to epsilon_0, if that means anything to you, which is the first ordinal that PA "can't handle".  i.e. can't prove that it is an ordinal, i.e. that
the above process must halt, (as it executes a decreasing series of ordinals, which therefore must always terminate).

You can see how the newly proposed budding chess emulates this slightly; there is an increasing number of pieces, but the total metric (in an appropriate sense) is always decreasing... i.e. the "top value".

Trabsact Sagme Diaries

The abstract game's fog should be adequate to the player's myopia [T.Sagme, Proverbs]

MONOCHROMATIC WHISTLING

MONOCHROMATIC WHISTLING

* On each turn, a player must either move or capture.
* A move is any number of unoccupied spaces in a straight line.
  A moved piece must end geometrically closer to at least one enemy piece.
* A capture is either
 (a) by whistling: a piece moves as above, and any enemy pieces
     which were adjacent to the line of movement, but not adjacent
     to the starting or finishing cell, are removed.
     Captures of this sort may be chained together (checkerswise).
 (b) by crushing: a piece adjacent to any enemy may capture and replace it.
* Capture is compulsory, with mandatory maximum capture (otherwise free).
* A player loses when he has no pieces left.
* After 20 consecutive non-capturing moves by each player, it is a draw.

Game Sample
    == XXX ==       == OOO ==
 1. s1-q1            h8-L8
 2. q1-i9:-c9: (f)   L8-C16:2-o1:2 (f)
 3. t2-l2:o1         g7-c11:c9
 4. i15-c9:c11 (f)   h6-b12:c9
 5. l2-e9:f6e7       x20-B20
 6. g15-b10:b12(f)   B20-M9:3  
 7. J15-M13          M9-N10
 8. v2-z2            N10-I15:M13-e15:2
 9. z2-L14:2         e15:f16 (f)
10. g17:f16          I7-M11
11. u1-A1            M11-G17::-r2:-D2:
12. resign

,'"abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNO
1            . . . . . . . . : . .          
2           . . . . , . . . . . o .          
3          . . . . . . : . . . . . .          
4         . . . . . . . . . . . . . .          
5        . . . . . . . . . . . . . o o          
6       . . . . . . . . . . . . . . o o          
7      . . . . . . . . . . . . . . . . .          
8     . . . . . . . . . . . . . . . . . .          
9    x x . . . . . . . . . . . . . . . . .          
10  x . . . . . . . . . . . . . . . . . . .          
11 . . . . . . . . . . . . . . . . . . . , .
12  . . . . . . . . . . . . . . . . . . . .          
13   . . . . . . . . . . . . . . . . . . .          
14    . . . . . . . . . . . . . . . . . :          
15     . . . . . . . . . . . . . . . . .          
16      x . . . . . . . . . . . . . . :          
17       . x . . . . . . . . . . . , .          
18        . . . . . . . . . . . . . .          
19         . . . . . . o o . . . . .          
20          . . . . . o o . . . . .                    
21           . . . . . o o . . . .                      
`-.abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNO

This is a game of sacrifices to obtain larger captures. There are two ways of capture, but the whistling mecanism is a novel idea due to Bill Taylor.

SAFE CHESS (another sample game)

Standard progressive, but mate may not be given except against a bared king.

Game sample:
. . . . . . . .  |  1. Nf3
. . . . p . . .  |  2. f5 Nf6
. . b k . p . .  |  3. N,:d8
. . . . . . . .  |  4. f4f3:e2:d1Q+
p . . . . . . .  |  5. K:d1 Ne6:f8:d7:f6+  
. . . . . . . .  |  6. g:f6 Rg8:g2:h2:h1:f1+
. . O . . O . .  |  7. Ke2:f1 a456:b:c8Q+
. . K . . . . .  |  8. Kf7 Nc6 R:c8b8:b2:b1:a1:c1+
                    9. Ke2 d456:c78Q:c6 Kd2:c1
                   10. h5h4h3h2h1B:c6 Ke6d6 a5a4

DESTROY AND BUD

1. Basic chess rules apply, except:
2. When a piece makes a capture, it buds off a piece one rank lower,
   leaving this behind on the exit square.  Ranks  KQRBNP-.

Game Sample:
                        
r . b . k . n r     |  1. e4    e5         10. Kg1  Rh:h2
p p p p . p p p     |  2. d4    Nc6        11. R:h2 Q:g3+
. . B . . . . .     |  3. d:e5  Bc5        12. resign!
. N n . r . . .     |  4. Bb5   B:f2
. . . . . . . b     |  5. K:f2  Qh4+
. . . . . O q .     |  6. g2    Q:e4    
O O O . r . . R     |  7. Nf3   N:e5  
R N B Q . . K B     |  8. N:e5  Q:e5  
                       9. B:c6  Re2+

As people can see in the game sample, the ploriferation of pieces allow for strong and dealy attacks against the adversary force. Since there is a demotion mechanism on the captures, the game converges to an end.

SPARTAN CHESS

Rules of FIDE chess, except:
Start with 30 pawns and 2 kings each (at d1e1/d8e8)
Goal: capture both opponent kings.

1222... progressive mutator. The two moves in a turn must be made with different pieces.
If one king is captured, the victim goes down to 1 move per turn.
Pawns may move 2 steps off 1st or 2nd row at any time, e.p. applies.
Whenever a piece makes a capture, it goes UP a step in power,
using the sequence P>N>B>R>Q>A(=QN). 8th-rank pawns promote to A.

Game sample:
                       White        Black
p . p k k p . p  1.  ---  d:e5   d:e5  g:f4
. p p p p p . .  2.  e:f4 e:d5   e:d5  N:d3
. . . . . p . b  3.  g:h5 a:b5   a:b5  g:h5
. . N . . p p .  4.  b:c5 c:d3   b:c5  n:f4
. n n . . O . .  5.  N:f4 c:d5   c:d4  h5  
. O K O O O O O  6.  a4   c4     N:f4  Nd4
. . . . . . . O  7.  g:f4 e3     N:a4  N:b3  
. . O . K O O O  8.  a:b3 N:h5   B:b3  g6
---------------- 9.  B:g6 a2     h:g6  Rb6
                10.  c3   f4     N:h4  a4
                11.  b:a4 Kc2    Rb4  Bg5
                12.  b3   g3     Bh6  b5
                13.  Nc5  d3     b7   g6  
                14.  a3   f3     a5   g5
                15.  a:b4 Kc3    a:b4 b:c4
This is a very enjoyable game, with lots of capturing action starting at turn 1, and then shifting to subtle positional battles in order to promote to Amazons (Queen + Knight power). The fact that each player has two Kings also add an extra complexity of trying to protect both for as long as possible.

FRAGILE WEAPON CHESS

  1. The FIDE rules apply, except:
  2. Captures by machine-gun or grenade, at mover's choice.
     (A moving piece need not make captures that are available, but any made must include all multiple hits of that type.)
     Machine gun means capturing all pieces on capture range without moving and grenade means capturing all adjacent pieces after the piece move.
  3. Capture REDUCES the capturing piece by a rank: Q>R>B>N>P
     Pawns that capture are thus removed.
     Kings capture without reduction of power.
  4. Win by killing king.
  5. Castling legal when pieces have not moved.

r . . . k . n r     |  1. e4     d5:
p p p . p p . p     |  2. Bd3    g6
. . n . . . . .     |  3. b4     Bg7
. . . . . . . .     |  4. c3     Bg4:
. . . . . . . .     |  5. Bf5::  Qd3::::
. . . . . . . .     |  6. Bd2:   Bc3:::
O . . K . O O O     |  7. Kd2:   Nc6
. . . . . . N R     |  8. resign

WEITUWEIQI (a game sample)

Oshiqi mechanics with both players playing "x"s. Chicken start.
Moves are mandatory, and if the game ends by stalemate then
the winner is determined by whether the boundary has been reached.
Any boundary hit is a win for an ESCAPER, otherwise BLOCKER wins.

Unlur or "chicken" starting:-  both sides play moves as ESCAPERS.
If at any time a player feels a blocker is now certain to win,
he announces "I Block!", but does not make a move. The other player
remains the sole escaper and plays the first move in regular alternation.

Note: If, still on the first phase, a player makes a stalemate position
he loses, (opponent chooses "block" and stalemater cannot continue).

Game sample
                             B    J
abcdefghijklmnopqrstu       ----------
     . . . x . .        1.  i6    s6
    . . . x . . .       2.  j5e   q6
   . . . . . x x .      3.  j7n   l1
  . x . . . . . . .     4.  p3    k2
 . . . x x . . . . .    5.  q8    o8
. . . . x . . . x x .   6.  n3!  block
 . . . O x . . . . .    7.  h5se  p11
  . . . : . . x x .     8.  p9    g10
   . . . X . . x .      9.  l11   e4
    . x . . . . .      10.  j9    l9 (forced)
     . . . x . x       11.  i2   1-0
abcdefghijklmnopqrstu

7x9 CHICKEN HEX (a quick game sample)

Players always drop isolated stones (ie, not adjacent to another) in the negotiation phase (in the diagram: x diagonal, o horizontal)

0: B d4, f2, d2, b2, f8, g9, a1, J takes x

x . . . . . .          1.  d6      a7?
 . x . x . x .         2.  c6      f5!
  . . . . . . .        3.  resigns
   . . . x . . .       4  
    . . . . . x .      5
     . . o o . . .     6  
      x . . . . . .    7
       . . . . . x .   8
        . . . . . . x  9
         a b c d e f g

SUICIDE BOMBER CHESS (a game sample)

Moves are only to empty squares, after which all opponent pieces
kingwise adjacent to the new position are destroyed; and if there are
any of those, the moving piece is also destroyed. Win by killing the
king (the "Osama"), who may not suicide. Castling is permissible
whenever the two pieces have not previously moved.

r . . . k . . r     |  1. Nc3   b5      10. Nd4   Nb4:
p . . . . p p p     |  2. a4:   Bb7     11. Rf2   c5:
. . . . . . . .     |  3. e4    e5:     12. Kf1   Qd1::
. . . . . . . .     |  4. Qe2+  Bf3:::  13. resign
. . . . . . . .     |  5. Bh3   Bb4:  
. . . . . . . .     |  6. Ne2   Nh6
. O : . . R . O     |  7. Rf1   Ng4:  
. . : . . K . .

Lovely 4 HexGomoku

Gomoku rules on hex board but each player must also drop an enemy stone as
close as possible to his own dropped stone. Wins by making a 4 in-a-row.

Game sample:

  ___oooo________xxxx___
1.  l25 n25     m24 o24
2.  o26 p27     k22 j21
3.  l23 k24     i24 j25
4.  g24 e24     h25 i26
5.  j23 h23     g22 i22
6.  f21 e20     f23 d23
7.  resigns

abcdefghijklmnopqrstuvwxyz

 . . . . . . . . . . . . . 19
. . x . . . . . . . . . .  20
 . . o . o . . . . . . . . 21
. . . x o x . . . . . . .  22
 . o x x o o . . . . . . . 23
. . x o x x x o . . . . .  24
 . . . x o o x . . . . . . 25
. . . . o . . o . . . . .  26
 . . . . . . . x . . . . . 27
. . . . . . . . . . . . .  28
 . . . . . . . . . . . . . 29

abcdefghijklmnopqrstuvwxyz

This variant, played on a hex board, has less directions to win (6 instead of the 8 on a square board) and that provides a better game, since on the square version it's much easier to win.

On the other hand, playing 5 in-a-row with the Love mutator seems very hard to force a win. The game tends to prolong itself without a final outcome.

134* TRICOLEUR HEXXAGON

Rules like Ataxx in a hex board (like Hexxagon, except:

There are three colors: A,B and C. A flips B which flips C which flips A (flips means the enemy piece becomes just like the moved piece, just like Ataxx). Also, a piece captures enemy pieces of the same type (ie, removes them from board).

Initial setup:

abcdefghijklmnopqrstuvwxyzABCDEFG
        A . . . b . . . c           1
       . . . . . . . . . .          2  
      . . . . . . . . . . .         3
     . . . . . . . . . . . .        4
    B . . . C . . . a . . . A       5
   . . . . . . . . . . . . . .      6
  . . . . . . . . . . . . . . .     7
 . . . . . . . ___ . . . . . . .    8
c . . . b . . /   \ . . B . . . C   9
 . . . . . . .\___/. . . . . . .   10
  . . . . . . . . . . . . . . .    11
   . . . . . . . . . . . . . .     12
    a . . . A . . . c . . . b      13
     . . . . . . . . . . . .       14
      . . . . . . . . . . .        15
       . . . . . . . . . .         16
        C . . . B . . . a          17
abcdefghijklmnopqrstuvwxyzABCDEFG

A player wins the game by eliminating one enemy color.

---

Game sample (abc even turns, ABC odd turns):

 1. k13                           abc ABC
 2. u13q13  w17     e13i13      
 3. j16     k13     q17m17 k1       9-12
 4. q1t2    j8      v6     D12     12-12
 5. m13k11  k15     m5p6   G9D8    12-13
 6. i9k7    j8l6    v6v8   s3      13-13
 7. l10     l14     B6     p6s5    12-17
 8. t2p2    t4      C11    w9      16-14
 9. l14p14  D8z8    l10l8  f4      13-17
10. t4x4    p2l2    w17u15 C11A9   16-15
11. b6b8    j6      n16    g3      13-21
12. x4A5    j2      y9w11  y9      17-17
13. B8x8    g3k3    l6o5   o15     12-19
14. s3q5    c9      A5y7   z16     16-18
15. o15s15  l2n4    k13o13 e5e7    14-20
16. C13z14  v12     z16B14 x2      16-20
17. u15x16  o5r6    o13s13 e7b8    12-24
18. x8v10   w3      v12x10 z14z16  15-22
19. s13u11  q13s11  r6u7   k11n12  14-23
20. x10t10  v10v12  x4     D12A11  17-20
21. p14s13  n12p14  u7u9   k7o7    16-20
22. v12t14  u11r12  w11s11 y5      17-20
23. t12     u9x8    o17    o7s7    14-24
24. y5w7    r14     x16t16 y17u17  16-21
25. s13s15  n16-n14 u7     v12     11-26
26. u17u15  y15     C5z6   C11     13-24
27. u7u9    t12v14  v12x14 w7y5    10-25
28. z16w15  z6z4    D10    z14     14-21
29. u9y9    r14v14  o17r16 s5      13-22
30. w3t4    B14B12  x14    x6      16-20
31. y9B10   r16t14  s5     s11u9   11-24
32. resigns

Final Position:

abcdefghijklmnopqrstuvwxyzABCDEFG
        c c . . . . . . b          1
       . B . . . . . . b .         2
      . . B . . . . . . . .        3
     B . . . B . . : . c c .       4
    . . . . . . B B . . c . .      5
   . . . A . . . . . . c . . .     6
  . . . . . . . . A . . . . . .    7
 B . . . . A . ___ . . . . . . .   8
B B . . . . . /   \ B . . . . . .  9
 . . . . . . .\___/. . . . A A .  10
  . . . . . . . . . . . . A A .   11
   . . . . . . . B . . . . a .    12
    . . . . . . . . . . . . .     13
     . . . . C . . C C a a .      14
      . . B . . . . . . . .       15
       . B . . . . . . . .        16
        B . C . . . . . .         17
abcdefghijklmnopqrstuvwxyzABCDEFG

This is a remarkable game, with lots of strategic planning in order to achieve local victories based on the deployment of its different units. An army configuration can be strong in one sector and vulnarable in another.

VERY SLOWLY PROGRESSIVE Y

Progressive Y (with the drop restriction of just one piece per friendly group per turn) with the following move sequence:1 2 2 2 3 4 4 4 5 6 6 6 7 8 8 8...

Game:

1.  k7 (X started)
2.  n8 k9
3.  j8 g9
4.  k5 n6
5.  m5 m7 f10
6.  m9 q9 h8  l6
7.  h6 o7 f8  o9
8.  h4 p6 p8  g7
9.  i3 i5 i9  l4  i11
10  i7 q7 h10 b10 m11 e11
11  j4 c9 j10 n10 t10 q11
12  m3 j2 o11 s11  j6 e9
13  l2 f6 l10 r10 c11
14  e6 d10 ...and wins next move.

Final position:

abcdefghijklmnopqrs
          .            1
         o x           2
        x . o          3
       o x x .         4
      . x o x .        5
     x x o o o o       6
    o o o x x x o      7
   . x o x . o o .     8
  x o x x o o x o .    9
 o o x o x x x . x x  10
. x o . x . o o x o . 11
abcdefghijklmnopqrstu 12

In most games (Go, Hex, Y, Moku...) the progressive variant without any restriction does not provide a propoer strategic background. In our experience, a progressive mutator sequence (and there are several, as we already saw during this blog) does have a very good partner, the group restriction mutator. Using both, each multiple drop within a turn is balanced so that no group of connected pieces is extended by more than one piece (except, of course, when two groups merge by placing one stone inbetween).