Mar 16, 2007

SLOWLY PROGRESSIVE ORTHODOX CHES

Each player plays moves for both colours,
in series 1 3, 3 3, 5 5, 5 7, 7 7, 9...
Every move must be legal for an orthodox chess game

Sample Game

1.   e4    * Nh6      
2. * Ke2   * Na6      
3.   Nc3     Nf5      
4.   e:f5  * h5      
5.   Qg4   * h:g4    
6.   h3      Nb8      
7.   h:g4    a6      
8.   R:h8  * f6      
9. * Rh6   * g:h6    
10. * Ke2   * Nc6      
11.   d3      h5
12.   g:h5    Bh6
13.   B:h6  * a4
14. * b4    * a:b
15. * Bc1   * R:a2
16. * Nb1   * R:a1
17.   Nc3     Ra2
18.   N:a2    Kf7
19.   N:b4    Qf8
20.   B:f8  * K:f8
21. * h6    * N:b4
22. * h7    * N:d3
23. * h8 N  * N:f2
24.   g4      Ke8
25.   g5      Kd8
26.   g6      Ke8
27.   g7      Kd8
28    g8Q++

Final Position

. . b k . . Q N
. p p p p . . .
. . . . . p . .
. . . . . O . .
. . . . . . . .
. . . . . . . .
. . O . K n . .
. . . . . B N .


This slower progressive sequence allows more strategy since mates are not so fast to achieve and, thus, tactical positions are possible to build and develop.

QUADREX

Players alternately drop one of their own stones onto any empty cell.
If this results in the formation of a small square with two similar
diagonal stones and one opposite stone, then the 4th cell is immediately
filled by the pair's color.  If this results in a similar situation,
the same applies again, and so on indefinitely.   One move equaliser.

The winner is whoever completes an orthogonal own-path in his direction.

Sample Game:

a b c d e f g h i j k l m n o p        Horz  Vert
. . . . . . . . . . . . . . . .   1.   l8    i8
. . . . . . . . . . . . . . . .   2.   i11   g10
. . , . . . . x . o o o . , . .   3.   h9    g8
. . . x . . o . . o x o . . . .   4.   g4    k6
. . . . , o . x x x x x . . . .   5.   l4    k4
. . . . o . x . o x x . . . . .   6.   j4    l5+
. . . . . o o o o o . . . . . .   7.   k3++  d4
. . . . . o x . x . . o . x . .   8.   e6    h5
. . . . . . . o . . . . . . . .   9.   f5    h3
. . . . . . x x x . . . . o . .  10.   h7    g6
. . . . . . x x o . . . . . . .  11.   f13   h12
. . . . , o o x . . . , . . . .  12.   h14   h13
. . . . . o x x o . . . . . . .  13.   h15   h16
. . , . . . x o o . . . . , . .  14.   g12   g11+
. . . . . . . o . . . . . . . .  15.   i13+  g14+-
. . . . . . . x . . . . . . . .  16.   f8    i10+
a b c d e f g h i j k l m n o p  17.   g7+   j6
                                 18.   i6 !  i5+
                                 19.   j7+   n8
                                 20.   n10   resign


This is a new connection game with lots of potential, using a novel mechanism to prevent the expected deadlocks of connections in orthogonal boards.

QUADRAPHAGES

In each turn a player
(a) moves his stones rookwise, the previous # of cells;
(b) announces a new number (between 1 and 8);
(c) moves his stones the new number of cells.

When a stone leaves a cell, it marks it with its own colour.
A stone may not land on a marked or occupied square, or leave the board.
Given a number, stone must move if it can, otherwise it remains stationary.
Intervening own-pieces or marks of either type do not block a move,
but opponent pieces do.  The first move begins with operation (b) & (c) only.

The game stops when all four stones in succession fail to move; then...
the winner is whoever has the most marked cells.

              _XX_                         _OO_
1.  ....  ....     ....  ....    ....  ....  8  g9g1  c1c9
2.  a7i7  i3a3  6  i7c7  a3g3    c9i9  g1a1  1  a1a2  i9h9
3.  g3f3  c7b7  6  f3f9  b7h7    a2g2  ----  1  h9h8  g2h2
4.  h7h6  f9f8  1  h6i6  f8g8    h2h3  h8h9  1  h3h4  ----
5.  g8g7  i6i5  3  i5i2  g7g4    h4h1  ----  6  h1b1  i8c8
6.  i2c2  g4a4  1  c2b2  a4b4    c8d8  ----  5  b1b6  d8d3

Current Position

a b c d e f g h i    
o o o . . . o o .  1  
o X x . . . o o x  2
x . . O . x x o x  3
x X . . . . x o .  4
. . . . . . . . x  5
. O . . . . . x x  6
x x x . . . x x x  7
. . o o . x x o o  8
. . o . . x o o o  9

Mar 6, 2007

1222 UNRESTRICTED 6-MOKU

Wins the player that makes a 6 in-a-row on an unlimited square board.
Each player moves twice, except in the first move where just one stone is dropped

Sample game ('o' starts):

1. --- o24    o23 n24
2. m25 n25    l25 m26
3. n27 o26    p24 p25
4. o27 p27    q27 q28
5. n26 p28    l24 q29
6. o28 n29    'x' resigns

i j k l m n o p q r s t
. . . . . . . . . . . . 20
. . . . . . . . . . . . 21
. . . . . . . . . . . . 22
. . . . . . x . . . . . 23
. . . x . x o x . . . . 24
. . . x o o . x . . . . 25
. . . . x o o . . . . . 26
. . . . . o o o x . . . 27
. . . . . . o o x . . . 28
. . . . . o . . x . . . 29
. . . . . . . . . . . . 30

Can you see why 'o' won the game?

Feb 22, 2007

DESTROY AND HYDRA-BUD (An example)

  1. Basic chess rules apply, except:
  2. When a non-royal piece makes a capture, it reduces rank and buds off a piece of that same lower rank, leaving this behind on the exit square.
Ranks  Q>R>B>N>P>(no piece)
 1. e4    e5    
 2. Qf3   f6    
 3. Bc4   Ne7    
 4. d4    d5    
 5. Bb5+  c6    
 6. Qc3   c:b5  
 7. Q:c8  Q:c8  
 8. R:c8  R:c8  
 9. Nf3   Bg4    
10. N:e5  B:f3+  
11. g:f3  d:e4  
12. Bf4   Nd5  
13. Bg3   N:c3  
14. b:c3  Ba5+  
15. O-O   Bb4  
16. e:f6  O-O
17. a3    Be1
18. Bd6   R:f2+
19. R:f2  B:d6
20. B:e1  N:f2+
21. K:f2  Ne4+
22. Ke2   Nc6
23. Nd3   Re8
24. Bg2   Nc3+
25. Kd2   N:b1Q++

Final Position:
. . . . r n k .
p p . . . . p p
. . n . . . . .
b . . p . . . .
. . . O . . p .
O . p N . . . .
. . O K . . B O
R q . . . . . .


A beautiful check mate

Feb 12, 2007

FRAGILE PROGRESSIVE CHESS

Basic progressive chess, with the following addition.
After every capture, a piece immediately reduces one rank in strength
before the series continues. Order Q R B N P -. Kings don't change.
(the order is: capture;reduce;promote;check;endmove)

Sample game:

1. e4
2. d5 e:d
3. Bc4:d7(N):d8P>Q+
4. K:d8 Bf4:d1(N):b2P
5. B:b2 Nc5b6:a8>Q:b8+
6. Kd7 e5 Ba3b2:a1>N b5
7. Nf3h4h5 Nc3d5:c7>Pc8>Q++

Final Position:

. R Q . . . n r
p . . k . . p p
. . . . . . . .
. p . . p N . .
. . . . . . . .
. . . . . . . .
O . O O . O O O
n . . . K . . R

Feb 8, 2007

A new way to play computer-Go?

Computers have started to outperform humans in games they used to lose [full text here]


[...] Deep Blue and its successors beat Mr Kasparov using the “brute force” technique. Rather than search for the best move in a given position, as humans do, the computer considers all white's moves—even bad ones—and all black's possible replies, and all white's replies to those replies, and so on for, say, a dozen turns. The resulting map of possible moves has millions of branches. The computer combs through the possible outcomes and plays the one move that would give its opponent the fewest chances of winning.

Unfortunately, brute force will not work in Go. First, the game has many more possible positions than chess does. Second, the number of possible moves from a typical position in Go is about 200, compared with about a dozen in chess. Finally, evaluating a Go position is fiendishly difficult. The fastest programs can assess just 50 positions a second, compared with 500,000 in chess. Clearly, some sort of finesse is required.

In the past two decades researchers have explored several alternative strategies, from neural networks to general rules based on advice from expert players, with indifferent results. Now, however, programmers are making impressive gains with a technique known as the Monte Carlo method. This form of statistical sampling is hardly new: it was originally developed in the Manhattan project to build the first nuclear bombs in the 1940s. But it is proving effective. Given a position, a program using a Monte Carlo algorithm contemplates every move and plays a large number of random games to see what happens. If it wins in 80% of those games, the move is probably good. Otherwise, it keeps looking.

This may sound like a lot of effort but generating random games is the sort of thing computers excel at. In fact, Monte Carlo techniques are much faster than brute force. Moreover, two Hungarian computer scientists have recently added an elegant twist that allows the algorithm to focus on the most promising moves without sacrificing speed.

The result is a new generation of fast programs that play particularly well on small versions of the Go board. In the past few months Monte Carlo-based programs have dominated computer tournaments on nine- and 13-line grids. MoGo, a program developed by researchers from the University of Paris, has even beaten a couple of strong human players on the smaller of these boards—unthinkable a year ago. It is ranked 2,323rd in the world and in Europe's top 300. Although MoGo is still some way from competing on the full-size Go grid, humanity may ultimately have to accept defeat on yet another front.

Copyright © 2007 The Economist Newspaper and The Economist Group. All rights reserved.

Feb 5, 2007

Kakuro

[from Nikoli website]


Write numbers from 1 to 9 on all white cells such that:
  1. A number in a cell separated by diagonal line tells the sum of numbers in consecutive cells at its right or downward.
  2. No number may appear more than once in consecutive cells.
Solution:

Jan 29, 2007

Yajilin

[from Nikoli website]

Draw a single line with a loop following the next rules:
  1. Lines must pass through the centers of cells horizontally or vertically and never cross, branch off, or go through the same cells twice.
  2. Cells where the line is drawn must not be black.
  3. Black cells must not touch each other horizontally or vertically.
  4. Lines don't go through numbered cells. Numbered cells cannot be black cells.
  5. Numbers represent how many black cells are at the direction of the arrow.
Solution:

Jan 26, 2007

ALTERNATING WEAPON CHESS

No-capture chess plus:

First player makes one move, then players make series of two moves until
captures are made, whereupon the series become of length three, etc.

Captures may be made as a series of one move only. The first capture
may be of either type, hand-grenade(*) or machine-gun(:), (which must
make the maximum number of takes available for that particular move);
and after that each player's capture types must alternate.

During a series of non-captures it is permissible to play a piece into
a position where it could make either sort of capture but does not do so,
at the mover's choice. Declaration of ambiguous capture type is unnecessary.

r . . . . Q . .     |  1. e4               11. Ng5::
. p k r . . b .     |  2. e5 Nc6           12. Bf6:
p . p . . R . .     |  3. Nf3 c3           13. f4* +
. . N p . . . .     |  4. d5*              14. Kf7e7d7c7
O . . O . . . .     |  5. Bb5: +           15. Nd2b3c5 Qg4
. . O . . . . .     |  6. c6:              16. Be6 Rf7d7 h6
. O . . . . O O     |  7. 0-0 d4 a4        17. Qg8::
R . . . . . K .     |  8. Be7 Nf6 O-O      18. Bg7*
____________________'  9. Bh6**            19. f5f6f7f8Q Rf6
                      10. Nh7*             20. resign

LOVE-Y

LOVE-L modifier:
Along with one's own stone one must play an opponent
stone as (Euclidean) close as possible to one's own.

          .            1.   n6  o5    m5 n4
         . .           2.   g7  f6    h6 g5
        . . .          3.   f8  e7    k7 m7
       . . . x         4.   l10 m11   j10 k11
      x . . o o        5.   j8  i9    i7 j6 !
     o o x . x .       6.   h8  g9    l8 n8
    o x o o x . .      7.   resign
   . x x x O X . .     8.  
  . . o o . . . . .    9.  
 . . . . o x . . . .  10.
. . . . . x o . . . . 11.  
abcdefghijklmnopqrstu


The 5th move for the second player finishes the game abruptly (a kind of mate in 6).

Jan 22, 2007

Ripple Effect

[from Nikoli website]


The areas, divided by bold lines, are called "Rooms". Fill in all empty cells with numbers under following rules:
  1. Each Room contains consecutive numbers starting from 1.
  2. If a number is duplicated in a row or a column, the space between the duplicated numbers must be equal or larger than the value of the number.
Solution:

Jan 19, 2007

Nonogram (aka Paint By Numbers)

  1. Paint some black cells such that they obey all numbers:
  2. Each number determines a number of consecutively filled squares (called a cluster).
  3. Each number sequence (row or column) shows how many clusters are there and the cluster sequence (naturally, each cluster is separated by, at least, one empty cell).
To read more, go to the Wikipedia entry.

Jan 18, 2007

Kurodoko

[from Nikoli website]

  1. Place black cells according to the next rules:
  2. Each number on the board represents the sum of white cells from that number to black cells or outer frame, horizontally and vertically.
  3. The cells which include numbers are always white.
  4. Black cells must not touch each other horizontally or vertically.
  5. All white cells must be orthogonally connected.
Solution:

Jan 16, 2007

Tentai Show

[from Nikoli website] [Wikipedia]

  1. Draw a bold line over the dotted line and divide the board into blocks.
  2. Every block must have horizontal and vertical symmetries with a star at its center.
Solution:

Jan 8, 2007

Number Link

[from Nikoli website]

  1. Connect same numbers with continuous line.
  2. Lines must go through the center of a cell horizontally or vertically and never go through twice the same cell.
  3. Lines cannot be crossed, branch off or go through number's cells.
Solution:

Jan 5, 2007

Shikaku (Divide by Box)

[from Nikoli website]

  1. Divide the grid into rectangles.
  2. Each rectangle contains only one number.
  3. The number indicates how many cells are contained in the rectangle.
Solution:

Jan 4, 2007

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:

Dec 28, 2006

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:

Dec 21, 2006

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:

Dec 15, 2006

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:

Dec 13, 2006

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:

Dec 12, 2006

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/

Dec 11, 2006

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/