1) If the ray hits an atom head-on then it is absorbed. This situation is marked with an
at the position where the ray went in.
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2) If the ray comes towards an atom one square off head-on, it gets deflected 90 degrees away from the atom. The entry and exit positions are marked with a 1 in the example on the right. Absorbing takes priority over deflecting, thus the second ray from the right side becomes absorbed.
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3) If the ray tries to pass between two atoms that are one square apart, it is reflected straight back. The ray will return to its entry position which will be marked with an
. This mark is also used if an atom is situated on the border and the ray goes in just one position beside the atom. In this case the ray is reflected even before it enters the board. This sitation is the most typical reason for a reflected ray. In the example to the right, four positions are marked from which fired rays have been reflected.
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4) If the ray is neither absorbed nor reflected, the positions where the ray enters and leaves the black box are marked with the same number (the number of the actual guess). Note, that the path of the ray may be arbitrarily complicated.
The worst score is always p*5 where p is the number of hidden atoms. This score can be achieved if no ray is fired at all and if the atoms are placed arbitrarely. Note also, that it is not always possible to find the hidden atoms from the information one gets through the rays. The simplest example for a molecule consisting of 5 atoms is given in the example to the right. The position of the fifth atom in the center can not be deduced. There exist also a few examples with 4 atoms. Can you construct one?
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The rules for playing BlackBox
The objective of the game is to find the form of a hidden molecule. The molecule consists of several atoms which are placed on the grid. To find out more about the hidden molecule, rays must be fired into the grid. The rays may be deflected or even absorbed by the atoms. From the position where a fired ray leaves the grid, the positions of the atoms have to be deduced. Only the reaction of the atoms on the fired rays is available, thus the name black box for this game.
Below, the possible influences of the atoms on the rays are described and illustrated with examples.
How to play BlackBox
To start the game, open the
BlackBox
dialog
. You may install a command into your menu to open this dialog. In the dialog you can define the size of the board and the number of atoms the computer will hide for you. When you click onto the OK button, a new window will appear which contains a new BlackBox puzzle. At the bottom of the view the number of hidden atoms is indicated.
To fire a ray into the grid, click into one of the locations on the edge of the grid. The result will be displayed immediately. Obviously this operation cannot be undone.
To tell the program where you think an atom is, click on the grid location. This will tentatively place an atom at that location. If you later decide that the atom should not be there, click on the square again, and it will disappear. When you think you have placed all of the atoms correctly, select Show Solution from the BlackBox menu and the computer will check the atoms that you placed and reveal any that you missed or placed incorrectly. In addition, a score will be displayed. The smaller the score, the better the result. Every ray which has been fired is counted with two points, except for absorbed and reflected ones which are only counted with one point. Additionally, for every misplaced atom five points are added. For an eight by eight board with four hidden atoms the average score is between ten and fifteen. Once the solution has been shown, you can visualize the path a ray will follow by clicking into the edge of the grid while holding down the modifier key.
If you execute the menu entry New Atoms, then the computer will hide a new molecule for you which consists of the same number of atoms as the last one.
If you want to generate a new puzzle for someone else, then place the atoms on the grid and select the Set New Atoms command. The number of the hidden atoms will be updated accordingly. You may save and mail such a puzzle to your friends.
Some background information
BlackBox has been invented by the English mathematician Dr. Eric W. Solomon. All the games he invented are distinguished by the fact that they are easy and simple, but very interesting. In other words, his games are in the spirit of Oberon, namely as simple as possible, but not simpler.
BlackBox got published in Germany under the names Logo and Ordo already in 1978 but was withdrawn already two years later. It is now again available from the franjos company under its original name BlackBox in a nice edition (wooden stones and atoms made out of glass). Other games invented by Solomon are Sigma File and Vice Versa. The latter has also been published under the name Hyle.
The objective of the game is not to deduce the hidden position of all atoms completely, but rather to score with as few points as possible. Thus, in some situation it may be better to apply some intuition than firing additional rays.
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