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    <p>Short and sweet, using a negative lookahead:</p> <pre><code>/^(?!.*([1-9]).*\1)[1-9]{9}$/ </code></pre> <ul> <li><code>[1-9]</code> is the character class for nonzero digits - equivalent to <code>[123456789]</code></li> <li><code>.*</code> matches any string of any length.</li> <li><code>.*([1-9]).*\1.*</code> matches any string with that contains at least two occurrences of the same nonzero digit <ul> <li>a nonzero digit is matched and captured by <code>([1-9])</code></li> <li>a repeat of that nonzero digit is matched by <code>\1</code>, a <strong>back-reference</strong> to the first captured match.</li> <li>the <code>.*</code> matches the arbitrary padding before, and between the nonzero digit and its repeat.</li> </ul></li> <li><code>(?!<i>&lt;pattern&gt;</i>)</code> matches any position where the contained pattern <em>doesn't</em> match. This is a <strong>negative lookahead</strong>, as it only matches a <em>position</em> in the string, and doesn't consume any of it - just looks ahead to compare it with the contained pattern.</li> <li><code>[1-9]{9}</code> matches nine nonzeo digits. <ul> <li><code><i>&lt;pattern&gt;</i>{9}</code> means match the preceding pattern 9 times.</li> </ul></li> <li><code>^<i>&lt;pattern&gt;</i>$</code> matches any string that exactly matches the contained pattern (rather than contains a substring that matches the pattern) <ul> <li><code>^</code> matches the position at the beginning of a string OR the beginning of a line</li> <li><code>$</code> matches the position at the end of a string OR the end of a line</li> </ul></li> </ul> <p>So combined, we check to make sure that it's not repeating any digits, then we check that it's only digits. Since it's 9 digits long, and none repeat, all must show up exactly once. That's the <a href="http://en.wikipedia.org/wiki/Pigeonhole_principle" rel="noreferrer">pigeonhole principle</a> at work!</p> <p>The syntax for your specific regular expression engine may vary. The above is a <a href="http://en.wikipedia.org/wiki/PCRE" rel="noreferrer">PCRE</a> (supported in Perl, Ruby, and a bunch of different other languages). <a href="http://en.wikipedia.org/wiki/Regular_expression#POSIX" rel="noreferrer">Posix regular expressions</a> have slightly different syntax. Not all engines support negative lookaheads, but most support back-references. Neither are part of the definition of formal theoretic regular expressions, but are very convenient.</p>
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    1. COnice +1 for the explanation
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    2. CO+1 for a succinct answer with great explanation, but I'd still stick with the non-regex approach for readability.
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