14.cpp

#include <list>
using namespace std;

list<int> A ={ 3,7 };

list<int>::iterator elf1 = A.begin();
list<int>::iterator elf2 = ++A.begin();

void move_A_iterator( list<int>::iterator & it, int steps ) {
	while( steps-- ) {
		++it;
		if( it == A.end() )
			it = A.begin();
	}
}

void simulate() {
	int sum = *elf1 + *elf2;
  
	if( sum >= 10 ) {
		A.push_back( 1 );
	}
	A.push_back( sum % 10 );

	int steps = *elf1 + 1;
	move_A_iterator( elf1, steps );

	steps = *elf2 + 1;
	move_A_iterator( elf2, steps );
}

void print_all() {
	for( auto it = A.begin(); it != A.end(); ++it ) {
		printf( "%d ", *it );
	}
	printf( "\n" );
}

int main() {
	int expected_amount =  9 + 10;
	
	while( A.size() < expected_amount ) {
		simulate();
	}

	//print_all();

	auto last_it = std::prev( A.end(), (10 + A.size()- expected_amount));
	for( int i=0; i < 10; ++i ) {
		printf( "%d", *last_it );
		++last_it;
	}
}