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Hexagonal Black Box - Designed by Eric W. Solomon

From Erik Arneson,
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An entry in the Deduction Game Design Competition

For 2 players

GOAL

One player, the "Setter," secretly records the position of 6 "atoms" in cells of the board (the "box").

This is most easily done on a small paper copy of the board. The opponent, the "Getter," tries to deduce the positions of the atoms by sending notional "rays" into the board, and the Setter reports where they emerge, or if they are absorbed and do not emerge.

When the Getter thinks he has deduced the positions he announces them for comparison with the Setter's record. The Getter gets a penalty score equal to the number of "ray-markers" used plus 10 points for each incorrectly placed atom. The players then change roles so that both obtain a penalty score.

The player with the SMALLEST penalty score wins.

DIAGRAM: Hexagonal Black Box Diagram

The diagram shows the board and all distinct types of ray deflection, reflection, and absorption. A description is included at the end of these rules.

Note that a ray may interact with a *whole series of atoms* before emerging from the board, but multiple interactions are not illustrated in the figure. Multiple interactions that offer the Setter opportunities for setting traps for his opponent.

GAMEPLAY

After the Setter has recorded his chosen atom positions, the Getter selects one of the INPUT ARROWS identifying the line along which his next ray will start. He marks this with a ray marker bearing a unique letter (or number).

The Setter consults his record and works out what would happen to the ray. If the ray emerges at a different point he places a ray marker with the SAME identifier on the OUTPUT ARROW.

Note that all rays are reversible so there is no need to have separate INPUT and OUTPUT arrows. If the ray is absorbed the Setter substitutes a plain BLACK ray marker at the INPUT point. If the ray is reflected back to its INPUT point the Setter substitutes a WHITE ray marker at the INPUT point.

Trial Atoms

The Getter continues to send rays into the board, and may use black Go stones to mark trial atom positions on the board. These may be adjusted as he thinks fit.

He might use white GO stones to mark positions where he is fairly certain that there are atoms. But use of the GO stones is ONLY mandatory when he announces his final solution to the Setter, and then there must be exactly 6 stones on the board. The Getter's penalty score is then assessed.

Ray Markers and Arrows

In the diagram, the input arrows have to be small for reasons of space. In a board game these should be larger to allow more space for the ray markers. A board 10 inches across is adequate.

The ray markers may be colored discs, 2 of the same color bearing the number 1 (or letter A), 2 of the same color bearing the number 2 (or letter B), and so on. There must also be some plain black and plain white discs for marking absorptions and reflections respectively.

Description of Ray Trajectories

Refer to the diagram. Starting at the top left and proceeding anticlockwise round the board an absorption, marked "A" here, results from a direct hit on any atom. A simple 60 degree deflection results from a close encounter with a single atom. This is shown here with 2 ray markers bearing a "D."

The next example is a "double" deflection of 120 degrees produced by two atoms. The ray markers also bear a "D" here.

The next example is for a reflection produced by two atoms. The ray marker bears "R" here. So far, these effects are quite logical from a physical point of view.

The final example of a reflection produced by a single atom at the edge of the board is a little more tricky.

Two examples of edge atom reflections are shown, with ray markers bearing an "R." The point is that these rays would begin to deflect at the instant they are produced. They would therefore be detected as outputs at their INPUT points, and so would appear to be reflections. Rays sent in from the two intervening input positions would be direct hits on the atom shown, and so would be absorbed.

Note from designer Eric W. Solomon: Credit is due to Paul Branch of Salt Lake City who encouraged me to extend my orthogonal version of Black Box.

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