Hmm .. this is almost too straightforward to post, but here goes ...
Statutory Warning: Spoilers ahead
using std::pair;
pair<int,int> getDigits(int num) {
return std::make_pair(num / 10, num % 10);
}
int gcd(int a, int b) {
assert(b <= a);
if (b == 0) {
return a;
} else {
return gcd(b, a % b);
}
}
pair<int,int> getReducedForm(int num, int den) {
int g = gcd(den, num);
return std::make_pair(num / g, den / g);
}
bool isCuriousFraction(int num, int den) {
// If (1) the numbers share digits, and (2) they can be reduced,
// then they form a 'curious fraction'
auto reducedForm = getReducedForm(num, den);
auto n = getDigits(num);
auto d = getDigits(den);
if ((n.second == 0 && d.second == 0) || n.first > d.second) {
return false;
}
auto curiousForm = getReducedForm(n.first, d.second);
if (n.second == d.first && curiousForm == reducedForm) {
return true;
} else {
return false;
}
}
int main() {
int numProduct = 1, denProduct = 1;
// Go through all pairs of two-digit numbers, where one is smaller than the other.
for (int den = 10; den < 100; ++den) {
for (int num = 10; num < den; ++num) {
if (isCuriousFraction(num, den)) {
std::cout << "Debug: found " << num << " / " << den << std::endl;
numProduct *= num;
denProduct *= den;
}
}
}
// For lowest common terms, divide both by GCD
std::cout << "Denominator of product = "
<< denProduct / gcd(denProduct, numProduct) << std::endl;
}
... and runs as follows
Debug: found 16 / 64
Debug: found 26 / 65
Debug: found 19 / 95
Debug: found 49 / 98
Denominator of product = <redacted>
(Sigh ... yes, its longer than some of the previous solutions, but it really didn't take me long to write it ... I think I'm developing a renewed appreciation for C++)