openct-tasks/bebras/2017/2017-FR-10-building-lights/index_ar.html

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<html>
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<meta charset="utf-8">
<title>2017-AR-10</title>
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"id": "http://castor-informatique.fr/tasks/2017/2017-FR-10-building-lights/",
"language": "ar",
"version": "ar.01",
"authors": "Arthur Charguéraud, Mathias Hiron, Nir Lavee, France-ioi",
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<h1>إنارة المبنى</h1>
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<div id="taskContent">
<p>قم بإنارة المبنى كما هو موضح بالشكل المطلوب. لإنارة صف أو عمود, قم بوضع الكارت الخاص به داخل الفتحات البيضاء بالأسفل. ثم قم بالتشغيل.</p>
<p>كل كارت <span class="medium hard">عدا الأخير</span> سوف يضيئ الصف أو العمود المكتوب عليه.</p>
<p class="medium hard"><b>الكارت الأخير سوف يقوم بعكس التيار الكهربي ليطفئ اللمبات المضيئة والعكس.</b></p>
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<div class="animTitle">المبنى</div>
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<div class="animTitle">الشكل المطلوب</div>
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<div id="solution">
<h2>Solution</h2>
<div class="easy">
<p>To reproduce the pattern, it was necessary to turn on the columns B and C, as well as the lines 3 and 4. The order did not matter. So we could write the following program :
<p>
<img src="Sol_easy_1.png">
</div>
<div class="medium">
<p> Initially, all the lights are already on. The only card that can have an effect is the last one. So we start with it to extinguish everything.
<p>Then there are two possible strategies.</p>
<p>(1) We turn on all the boxes that are lighted in the objective figure, then turn off the ones we lighted too.</p>
<p>We start by turning on the columns A and D. We must then turn off the lines 5 and 2. For this, we reverse everything, we turn on the lines 5 and 2, then we reverse everything again.
<p>
<img src="Sol_medium_1.png">
<p>(2) We turn on all the boxes that are off in the objective figure, then we turn all the lights.</p>
<img src="Sol_medium_2.png">
</div>
<div class="hard">
<p>There are many possible solutions.</p>
<p>A first solution consists of the following steps:
<ul>
<li>Turn off the only lighted box that is not lighted in the objective figure, on line 2: <br/> reverse everything, turn on line 2, reverse everything.
<li>Turn on all the boxes that are in the objective: <br/> turn on columns A and D, lines 5.
<li>Turn off all the boxes that have been turned on too :<br/>reverse all, turn on the lines 0, 1 and 6, reverse all.
</ul>
</p>
<p>
<img src="Sol_hard_1.png">
<p>Below is the shortest solution. </p>
<img src="Sol_hard_2.png">
</div>
<h2>It's computer science !</h2>
<p> In this topic, each box of the building is on or off. Similarly, a computer's memory consists of <b> bits </b> whose value is either <b> 0 </b> or <b> 1 </b>. All numbers, all images, all texts, and all programs are described only with bits, that is, with long sequences of <b> 0 </b> and <b> 1 </b>. </p>
<p> At the heart of the computer is a <b> processor </b> that is able to handle bit packets, typically <b> 64 </b> bits, very efficiently. For example, the processor has a "reverse all bits" operation, which takes a 64-bit packet, and a fraction of a second, replaces all <b> 0 </b> with <b> 1 </b> and all <b> 1 </b> with <b> 0 </b>. A computer can perform more than two billion such operations on 64-bit packets in one second, manipulating over 100 billion bits in a single second !</p>
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