statement.html

problem 43 · 12 lines

<div class="problem_content" role="problem">
<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>
<p>Let $d_1$ be the $1$<sup>st</sup> digit, $d_2$ be the $2$<sup>nd</sup> digit, and so on. In this way, we note the following:</p>
<ul><li>$d_2d_3d_4=406$ is divisible by $2$</li>
<li>$d_3d_4d_5=063$ is divisible by $3$</li>
<li>$d_4d_5d_6=635$ is divisible by $5$</li>
<li>$d_5d_6d_7=357$ is divisible by $7$</li>
<li>$d_6d_7d_8=572$ is divisible by $11$</li>
<li>$d_7d_8d_9=728$ is divisible by $13$</li>
<li>$d_8d_9d_{10}=289$ is divisible by $17$</li>
</ul><p>Find the sum of all $0$ to $9$ pandigital numbers with this property.</p>
</div>