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<title>A.I.19.9</title>
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<div class="feladat">
<b>Feladat: 19.9.</b><br /> <a name="algI_GHP_426_teszt" />[<a href="bib_box.php?mode=sne-s-j-&amp;citation_num=65" target="bib_box" onclick="mutat('bib_box.php?mode=sne-s-j-&amp;citation_num=65'); return false;">65</a>] Egy szabályos <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>n</m:mi></m:mrow></m:math>-szögnek ötször annyi átlója van, mint oldala. Mekkora lehet az <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>n</m:mi></m:mrow></m:math>?

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Az <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>n</m:mi></m:mrow></m:math> szám utolsó jegye tízes számrendszerben:

<br /><b>A)</b>&nbsp;&nbsp;&nbsp; <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>0</m:mn></m:mrow></m:math> vagy <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>1</m:mn></m:mrow></m:math>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<b>B)</b>&nbsp;&nbsp;&nbsp; <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>2</m:mn></m:mrow></m:math> vagy <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>3</m:mn></m:mrow></m:math>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <b>C)</b>&nbsp;&nbsp;&nbsp; <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>4</m:mn></m:mrow></m:math> vagy <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>5</m:mn></m:mrow></m:math>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <b>D)</b>&nbsp;&nbsp;&nbsp; <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>6</m:mn></m:mrow></m:math> vagy <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>7</m:mn></m:mrow></m:math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<b>E)</b>&nbsp;&nbsp;&nbsp; <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>8</m:mn></m:mrow></m:math> vagy <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>9</m:mn></m:mrow></m:math><br />

y default: it reads from stdin and writes to stdout.

But a non-switch argument specifies the file[.tex] to translate to file.xml.

Diagnostics concerning unknown or untranslated constructs are sent to stderr.

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  Obtain USAGE </td><td width="150">

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  Obtain QUALIFICATIONS by:               ttm -?q

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<div class="feladat">
<a name="_solution_algI_GHP_426_teszt" /><b>Megoldás: 19.9</b><br />
<b>B</b>

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<br />

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    <m:math xmlns="http://www.w3.org/1998/Math/MathML">

    <m:mstyle displaystyle="true"><m:mrow>

<m:mfrac><m:mrow><m:mi>n</m:mi><m:mo>&middot;</m:mo><m:mo stretchy="false">(</m:mo><m:mi>n</m:mi><m:mo>-</m:mo><m:mn>3</m:mn><m:mo stretchy="false">)</m:mo></m:mrow>

<m:mrow><m:mn>2</m:mn></m:mrow>

</m:mfrac>

<m:mo>=</m:mo><m:mn>5</m:mn><m:mi>n</m:mi><m:mo>,</m:mo><m:mi>&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;</m:mi><m:mi>n</m:mi><m:mo>&middot;</m:mo><m:mo stretchy="false">(</m:mo><m:mi>n</m:mi><m:mo>-</m:mo><m:mn>3</m:mn><m:mo stretchy="false">)</m:mo><m:mo>=</m:mo><m:mn>10</m:mn><m:mi>n</m:mi><m:mo>.</m:mo></m:mrow>

    </m:mstyle></m:math>

</td></tr></table>

<br />

<m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>n</m:mi><m:mo>=</m:mo><m:mn>0</m:mn></m:mrow></m:math> nem értelmes a feladatban, így leoszthatunk <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>n</m:mi></m:mrow></m:math>-nel: <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>n</m:mi><m:mo>-</m:mo><m:mn>3</m:mn><m:mo>=</m:mo><m:mn>10</m:mn></m:mrow></m:math>, azaz <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>n</m:mi><m:mo>=</m:mo><m:mn>13</m:mn><m:mo>.</m:mo></m:mrow></m:math>

Egy szab. tizenháromszögnek 65 átlója van és 13 oldala, tehát ez valóban megoldás. 
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