158 lines
5.9 KiB
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158 lines
5.9 KiB
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<h2>Exploring Pascal's triangle.</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 148</h3><span style="width:300px;color:#666;">Published on Saturday, 7th April 2007, 02:00 am; Solved by 2576</span></div>
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<p>We can easily verify that none of the entries in the first seven rows of Pascal's triangle are divisible by 7:</p>
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<table cellpadding='0' cellspacing='0' border='0' align='center'>
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<tr>
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<td> </td>
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<td> </td>
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<td> </td>
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<td> </td>
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<td> </td>
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<td> </td>
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<td> 1</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td> </td>
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<td> </td>
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<td> </td>
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<td> 1</td>
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<td> </td>
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<td> 1</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td> </td>
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<td> </td>
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<td> 1</td>
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<td> </td>
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<td> 2</td>
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<td> </td>
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<td> 1</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td> </td>
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<td> 1</td>
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<td> </td>
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<td> 3</td>
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<td> </td>
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<td> 3</td>
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<td> </td>
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<td> 1</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td> 1</td>
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<td> </td>
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<td> 4</td>
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<td> </td>
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<td> 6</td>
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<td> </td>
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<td> 4</td>
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<td> </td>
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<td> 1</td>
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</tr>
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<tr>
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<td> </td>
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<td> 1</td>
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<td> </td>
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<td> 5</td>
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<td> </td>
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<td>10</td>
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<td> </td>
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<td>10</td>
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<td> </td>
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<td> 5</td>
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<td> </td>
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<td> 1</td>
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</tr>
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<tr>
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<td>1</td>
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<td> </td>
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<td> 6</td>
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<td> </td>
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<td>15</td>
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<td> </td>
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<td>20</td>
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<td> </td>
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<td>15</td>
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<td> </td>
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<td> 6</td>
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<td> </td>
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<td> 1</td>
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</tr>
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</table>
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<p>However, if we check the first one hundred rows, we will find that only 2361 of the 5050 entries are <i>not</i> divisible by 7.</p>
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<p>Find the number of entries which are <i>not</i> divisible by 7 in the first one billion (10<sup>9</sup>) rows of Pascal's triangle.</p>
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