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1<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN"
2"http://www.w3.org/TR/html4/strict.dtd">
3<html>
4<head>
5<meta http-equiv="content-type" content="text/html; charset=US-ASCII">
6<title>Black Box</title>
7<link rel="previous" href="untangle.html">
8<link rel="ToC" href="index.html">
9<link rel="up" href="index.html">
10<link rel="index" href="docindex.html">
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12</head>
13<body>
14<p><a href="untangle.html">Previous</a> | <a href="index.html">Contents</a> | <a href="docindex.html">Index</a> | <a href="slant.html">Next</a></p>
15<h1><a name="C19"></a>Chapter 19: <a name="i0"></a>Black Box</h1>
16<p>
17A number of balls are hidden in a rectangular arena. You have to deduce the positions of the balls by firing lasers positioned at the edges of the arena and observing how their beams are deflected.
18</p>
19<p>
20Beams will travel straight from their origin until they hit the opposite side of the arena (at which point they emerge), unless affected by balls in one of the following ways:
21</p>
22<ul><li>
23A beam that hits a ball head-on is absorbed and will never re-emerge. This includes beams that meet a ball on the first rank of the arena.
24</li>
25<li>
26A beam with a ball in its front-left square and no ball ahead of it gets deflected 90 degrees to the right.
27</li>
28<li>
29A beam with a ball in its front-right square and no ball ahead of it gets similarly deflected to the left.
30</li>
31<li>
32A beam that would re-emerge from its entry location is considered to be &#8216;reflected&#8217;.
33</li>
34<li>
35A beam which would get deflected before entering the arena by a ball to the front-left or front-right of its entry point is also considered to be &#8216;reflected&#8217;.
36</li>
37</ul>
38<p>
39Beams that are reflected appear as a &#8216;R&#8217;; beams that hit balls head-on appear as &#8216;H&#8217;. Otherwise, a number appears at the firing point and the location where the beam emerges (this number is unique to that shot).
40</p>
41<p>
42You can place guesses as to the location of the balls, based on the entry and exit patterns of the beams; once you have placed enough balls a button appears enabling you to have your guesses checked.
43</p>
44<p>
45Here is a diagram showing how the positions of balls can create each of the beam behaviours shown above:
46</p>
47<pre><code> 1RHR----
48|..O.O...|
492........3
50|........|
51|........|
523........|
53|......O.|
54H........|
55|.....O..|
56 12-RR---
57</code></pre>
58<p>
59As shown, it is possible for a beam to receive multiple reflections before re-emerging (see turn 3). Similarly, a beam may be reflected (possibly more than once) before receiving a hit (the &#8216;H&#8217; on the left side of the example).
60</p>
61<p>
62Note that any layout with more than 4 balls may have a non-unique solution. The following diagram illustrates this; if you know the board contains 5 balls, it is impossible to determine where the fifth ball is (possible positions marked with an <code>x</code>):
63</p>
64<pre><code> --------
65|........|
66|........|
67|..O..O..|
68|...xx...|
69|...xx...|
70|..O..O..|
71|........|
72|........|
73 --------
74</code></pre>
75<p>
76For this reason, when you have your guesses checked, the game will check that your solution <em>produces the same results</em> as the computer's, rather than that your solution is identical to the computer's. So in the above example, you could put the fifth ball at <em>any</em> of the locations marked with an <code>x</code>, and you would still win.
77</p>
78<p>
79Black Box was contributed to this collection by James Harvey.
80</p>
81<h2><a name="S19.1"></a>19.1 <a name="i1"></a>Black Box controls</h2>
82<p>
83To fire a laser beam, left-click in a square around the edge of the arena. The results will be displayed immediately. Clicking or holding the left button on one of these squares will highlight the current go (or a previous go) to confirm the exit point for that laser, if applicable.
84</p>
85<p>
86To guess the location of a ball, left-click within the arena and a black circle will appear marking the guess; click again to remove the guessed ball.
87</p>
88<p>
89Locations in the arena may be locked against modification by right-clicking; whole rows and columns may be similarly locked by right-clicking in the laser square above/below that column, or to the left/right of that row.
90</p>
91<p>
92The cursor keys may also be used to move around the grid. Pressing the Enter key will fire a laser or add a new ball-location guess, and pressing Space will lock a cell, row, or column.
93</p>
94<p>
95When an appropriate number of balls have been guessed, a button will appear at the top-left corner of the grid; clicking that (with mouse or cursor) will check your guesses.
96</p>
97<p>
98If you click the &#8216;check&#8217; button and your guesses are not correct, the game will show you the minimum information necessary to demonstrate this to you, so you can try again. If your ball positions are not consistent with the beam paths you already know about, one beam path will be circled to indicate that it proves you wrong. If your positions match all the existing beam paths but are still wrong, one new beam path will be revealed (written in red) which is not consistent with your current guesses.
99</p>
100<p>
101If you decide to give up completely, you can select Solve to reveal the actual ball positions. At this point, correctly-placed balls will be displayed as filled black circles, incorrectly-placed balls as filled black circles with red crosses, and missing balls as filled red circles. In addition, a red circle marks any laser you had already fired which is not consistent with your ball layout (just as when you press the &#8216;check&#8217; button), and red text marks any laser you <em>could</em> have fired in order to distinguish your ball layout from the correct one.
102</p>
103<p>
104(All the actions described in <a href="common.html#S2.1">section 2.1</a> are also available.)
105</p>
106<h2><a name="S19.2"></a>19.2 <a name="i2"></a>Black Box parameters</h2>
107<p>
108These parameters are available from the &#8216;Custom...&#8217; option on the &#8216;Type&#8217; menu.
109</p>
110<dl><dt>
111<em>Width</em>, <em>Height</em>
112</dt>
113<dd>
114Size of grid in squares. There are 2 &#215; <em>Width</em> &#215; <em>Height</em> lasers per grid, two per row and two per column.
115</dd>
116<dt>
117<em>No. of balls</em>
118</dt>
119<dd>
120Number of balls to place in the grid. This can be a single number, or a range (separated with a hyphen, like &#8216;2-6&#8217;), and determines the number of balls to place on the grid. The &#8216;reveal&#8217; button is only enabled if you have guessed an appropriate number of balls; a guess using a different number to the original solution is still acceptable, if all the beam inputs and outputs match.
121</dd>
122</dl>
123
124<hr><address></address></body>
125</html>