A Munchausen number is a natural number n the sum of whose digits (in base 10), each raised to the power of itself, equals n.

(Munchausen is also spelled: Münchhausen.)

For instance:    3435 = 33 + 44 + 33 + 55 



Task
Find all Munchausen numbers between   1   and   5000.



Also see

 The OEIS entry:  A046253
 The Wikipedia entry:  Perfect digit-to-digit invariant, redirected from Munchausen Number


 
#include <math.h>
#include <iostream>
 
unsigned pwr[10];
 
unsigned munch( unsigned i ) {
    unsigned sum = 0;
    while( i ) {
        sum += pwr[(i % 10)];
        i /= 10;
    }
    return sum;
}
 
int main( int argc, char* argv[] ) {
    for( int i = 0; i < 10; i++ )
        pwr[i] = (unsigned)pow( (float)i, (float)i );
    std::cout << "Munchausen Numbers\n==================\n";
    for( unsigned i = 1; i < 5000; i++ )
        if( i == munch( i ) ) std::cout << i << "\n";
    return 0;
}
 