81 lines
5.3 KiB
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81 lines
5.3 KiB
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<h2>Sub-string divisibility</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 43</h3><span style="width:300px;color:#666;">Published on Friday, 9th May 2003, 06:00 pm; Solved by 25542</span></div>
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<p>The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it also has a rather interesting sub-string divisibility property.</p>
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<p>Let <i>d</i><sub>1</sub> be the 1<sup>st</sup> digit, <i>d</i><sub>2</sub> be the 2<sup>nd</sup> digit, and so on. In this way, we note the following:</p>
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<li><i>d</i><sub>2</sub><i>d</i><sub>3</sub><i>d</i><sub>4</sub>=406 is divisible by 2</li>
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<li><i>d</i><sub>3</sub><i>d</i><sub>4</sub><i>d</i><sub>5</sub>=063 is divisible by 3</li>
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<li><i>d</i><sub>4</sub><i>d</i><sub>5</sub><i>d</i><sub>6</sub>=635 is divisible by 5</li>
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<li><i>d</i><sub>5</sub><i>d</i><sub>6</sub><i>d</i><sub>7</sub>=357 is divisible by 7</li>
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<li><i>d</i><sub>6</sub><i>d</i><sub>7</sub><i>d</i><sub>8</sub>=572 is divisible by 11</li>
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<li><i>d</i><sub>7</sub><i>d</i><sub>8</sub><i>d</i><sub>9</sub>=728 is divisible by 13</li>
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<li><i>d</i><sub>8</sub><i>d</i><sub>9</sub><i>d</i><sub>10</sub>=289 is divisible by 17</li>
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<p>Find the sum of all 0 to 9 pandigital numbers with this property.</p>
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