Ankor Cameron Browne (c) 2008

Ankor is a 3D connection game played with cubes.

Rules

Equipment: Two players, White and Blue, each have 28 cubes of their colour.

The board is a triangular grid of triangular holes (six per side), where each hole will snugly hold a cube placed corner-downward.

Start: The board is initially empty. White places a cube on the hole of their choice, then Blue may elect to swap colours in lieu of making the second move (swap option).

Play: Players then take turns either:
1) adding a cube of their colour to an empty board hole, or
2) moving a cube of their colour to a valid destination point.

A destination point is valid if it can be reached through a series of connected or adjacent steps through friendly pieces (two pieces are connected if they visibly share a face). The destination point need not be connected to the source point after the move.

If the cube being moved directly supports a single column, then the higher cubes in that column will naturally drop down to fill the gap. Cubes that directly support more than one column cannot be moved.

For example, Figure 1 (left) shows the four valid destination points to which piece a may be moved by White. Moving a to a' leaves a gap (middle), which is filled by the previously supported pieces sliding down (right).

Figure 1.  Valid moves for piece a, move to a' leaves a gap... which is filled by the dropping column.

Aim: The game ends as soon as a player forms a connected path of their colour that touches at least the tip of each board side. For example, Figure 2 shows a game won by Blue who has formed a path between all three board sides (this path only touches a tip of the bottom side).

Figure 2.  A game won by Blue.

Notes

Ankor is essentially Akron played with a hexagonal stacking of tilted cubes. Akron was in fact originally designed for the hexagonal grid until phase problems were discovered; the tilted cube stacking solves these problems. The Abstract Games magazine article posted on the official Akron page has more details.

It is possible for games to deadlock and not produce a winner (Figure 3), however this is extremely rare.

Figure 3.  A tied game.

Movable cubes are guaranteed to have at least two exposed faces (as they can only support one column), making it easier for the mover to get a grip on them.

The maximum number of cubes required for a given board size is given by the tetrahedral number Tn = n (n + 1) (n + 2) / 6.

Ankor rules copyright Cameron Browne © 2008.

The name “Ankor” is a reworking of "Akron"... which is more or less what the game is.

The Boche board with six holes per side is equivalent to the Foursite 3D board available from IQideas Ltd.

Boche can be played on Richard's PBeM server - check out the help file for more details. Many thanks to the server regulars who helped test the game. Please challenge me (camb) to a game any time.