I'm embarassed at how ridiculously naive my solution is. In hindsight, it's so obvious that the solution has to be a four-digit number and its double, and that the first digit is going to be a 9.
Still, C++ makes you lazy. This took 24 milliseconds, and I didn't feel the need to speed it up :)
Statutory Warning: Spoilers ahead
static const long kMaxNumbers = 10000;
int main() {
long largestPanDigital = 0;
for (long num = 2; num < kMaxNumbers; ++num) {
vector<int> pandigits;
int o = 1;
while (o <= 20) {
long product = num * o;
vector<int> pd;
while (product > 0) {
int d = product % 10;
if (d == 0 ||
(std::find(pandigits.begin(), pandigits.end(), d) != pandigits.end()) ||
(std::find(pd.begin(), pd.end(), d) != pd.end())) {
break;
}
pd.push_back(d);
product /= 10;
}
if (product > 0) {
// Found an existing digit
break;
}
// We formed a new product; keep going!
for (auto it = pd.rbegin(); it != pd.rend(); ++it) {
pandigits.push_back(*it);
}
++o;
}
if (pandigits.size() == 9 && o > 1) {
long panDigital = 0L;
std::cout << "Found: ";
for (auto& d : pandigits) {
std::cout << d;
panDigital = panDigital * 10 + d;
}
std::cout << " = " << num << " * " << o-1 << std::endl;
if (panDigital > largestPanDigital) {
largestPanDigital = panDigital;
}
}
}
std::cout << "The largest one is " << largestPanDigital << std::endl;
}
It runs as follows:
$ ~/cpp/Test
Found: 918273645 = 9 * 5
Found: 192384576 = 192 * 3
Found: 219438657 = 219 * 3
Found: 273546819 = 273 * 3
Found: 327654981 = 327 * 3
Found: 672913458 = 6729 * 2
Found: 679213584 = 6792 * 2
Found: 692713854 = 6927 * 2
Found: 726914538 = 7269 * 2
Found: 729314586 = 7293 * 2
Found: 732914658 = 7329 * 2
Found: 769215384 = 7692 * 2
Found: 792315846 = 7923 * 2
Found: 793215864 = 7932 * 2
Found: 926718534 = 9267 * 2
Found: 927318546 = 9273 * 2
Found: 932718654 = 9327 * 2
The largest one is <redacted>