CASTLE

Copyright (c) 2004 Martin WindischerThis game is played on the following board.

One player is the constructive player, the other one is the destructive player. The constructive player begins.

TURN- On each turn, each player picks the top stone of one stack and put it on the top of an adjacent stackof the same size.

The single stone of any stack of size one can only be picked if it is free, i.e., the stone is either on a corner or an edge or there are at least two adjacent empty cells (these two cells have to be adjacent too). GOAL- The game ends if there is no move left. The constructive player wins if there are at least 3 stacks of size 4 or one stack of size 5 or more. Else the destructive player wins.

An exampleThe constructive player can win by playing B3-C3 (any other move loses), because then the destructive player has to play E4-E5 or E5-E4 (he cannot move C5 or D5 because they are not free).

Now the constructive player can move E5-D4 or E4-D4. As there are two adjacent stacks of size 4 now, the destructive player cannot prevent a stack of size 5.

A game sampleConst Destr

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1. f6-e5 a4-b4

2. c6-c5 a1-b1

3. a2-b2 d6-e6

4. e6-e5 f5-f4

5. e2-d2 c1-d1

6. b1-b2 d2-d1

7. b1-c2 f3-e3

8. e3-f4 e3-d3

9. d3-c2 d2-d3

10. c2-b2 c2-d3

11. c2-c3 b4-c5

12. a3-b4 e6-d5

13. b3-c4 c4-b4? (c3-c4 wins Destr)

14. c5-b4 d5-c5

15. d5-c4 resign 1-0This position (check left diagram) is a win for the constructor. There no way to stop the making of a stack of size 3 between c3 and c4 and so to make a third stack of size 4 (and thus winning).

Another game sampleConst Dest

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1. f6-e5 e6-d6

2. c6-c5 b5-a4

3. a2-a3 b1-a1

4. d6-c5 f5-e4

5. c1-d2 c2-b2

6. f4-e3 e4-e5

7. d1-e2 a1-b2

8. d2-e3 e4-d3

9. a4-a3 a4-b4

10. resign 0-1Constructor resigns since there are very few legal moves and it is already impossible to achieve one of the goals.