/*
 * Sum-product problem (Erich Friedman version) solver
 */

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

int sums[17];
int products[81];
int i, j, x, y, p, s, u, v, r, count;

void init()
{
    for (i = 0; i < 17; i++) sums[i] = i + 1;
    for (i = 0; i < 81; i++) {
        p = i + 1;
        r = (int)sqrt(p);
        count = 0;
        for (u = 1; u <= r; u++) {
            if (p % u == 0 && u <= 9 && (p/u) <= 9) {
                count++;
            }
        }
        products[i] = (count > 1) ? p : 0;
    }
}

void S_does_not_know()
{
    for (i = 0; i < 17; i++) {
        s = sums[i];
        if (!s) continue;
        count = 0;
        for (u = 1; u <= (s/2); u++) {
            v = s - u;
            if (u > 9 || v > 9) continue;
            p = u * v;
            for (j = 0; j < 81; j++) {
                if (products[j] == p) count++;
            }
        }
        if(count < 2) sums[i] = 0;
    }
}

void P_does_not_know()
{
    for (i = 0; i < 81; i++) {
        p = products[i];
        if (!p) continue;
        r = (int)sqrt(p);
        count = 0;
        for (u = 1; u <= r; u++) {
            v = p / u;
            if (u > 9 || v > 9) continue;
            s = u + v;
            for (j = 0; j < 18; j++) {
                if (sums[j] == s) count++;
            }
        }
        if (count < 2) products[i] = 0;
    }
}

void P_knows()
{
    for (i = 0; i < 81; i++) {
        p = products[i];
        if (!p) continue;
        r = (int)sqrt(p);
        count = 0;
        for (u = 1; u <= r; u++) {
            v = p / u;
            if (u > 9 || v > 9) continue;
            s = u + v;
            for (j = 0; j < 18; j++) {
                if (sums[j] == s) { 
                    count++; 
                    x = u; 
                    y = v;
                }
            }
        }
        if (count == 1) {
            printf("The two numbers are %d and %d.\n", x, y);
            return;
        }
    }
}

int main()
{
    init();
    P_does_not_know();
    S_does_not_know();
    P_does_not_know();
    S_does_not_know();
    P_does_not_know();
    S_does_not_know();
    P_does_not_know();
    S_does_not_know();
    P_knows();

    return 0;
}