Question for Allen

/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Description: Finds all multiplications of the form * * * * * * * x * * * * * ------- * * * * * * * * * * * * * * * * * * * * ---------------- * * * * * * * * * * that satisfy the following conditions: * * - each star stands for a digit, with the leftmost star * * on each line standing for a nonzero digit; * * - all partial products are made up of the same digits; * * - the first and second partial products are different; * * - the orderings of digits in the second and third * * partial products are inverse of each other; * * - the third partial product is the sum of the first two * * partial products. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */ #include <stdio.h> #include <stdlib.h> int main(void) { for (int m = 100; m < 1000; ++m) for (int n = 100; n < 1000; ++n) { int product = m * n; if (product < 100000) continue; int partial_product1 = m * (n % 10); if (partial_product1 < 1000) continue; int partial_product2 = m * (n / 10 % 10); if (partial_product2 < 1000) continue; if (partial_product1 == partial_product2) continue; int partial_product3 = m * (n / 100); if (partial_product3 < 1000) continue; if (partial_product3 != partial_product1 + partial_product2) continue; /* Write first partial product as p11 p12 p13 p14. */ int p11 = partial_product1 / 1000; int p12 = partial_product1 / 100 % 10; int p13 = partial_product1 / 10 % 10; int p14 = partial_product1 % 10; /* Write second partial product as p21 p22 p23 p24. */ int p21 = partial_product2 / 1000; int p22 = partial_product2 / 100 % 10; int p23 = partial_product2 / 10 % 10; int p24 = partial_product2 % 10; /* Write third partial product as p31 p32 p33 p34. */ int p31 = partial_product3 / 1000; int p32 = partial_product3 / 100 % 10; int p33 = partial_product3 / 10 % 10; int p34 = partial_product3 % 10; /* Check that ordering of digits in second and third partial products * are inverse of each other. */ if (p21 != p34 || p22 != p33 || p23 != p32 || p24 != p31) continue; /* Set the p11-th, p12-th, p13-th and p14-th bits of digits_1 to 1. */ int digits_1 = 1 << p11; digits_1 |= 1 << p12; digits_1 |= 1 << p13; digits_1 |= 1 << p14; /* Set the p21-th, p22-th, p23-th and p24-th bits of digits_2 to 1. */ int digits_2 = 1 << p21; digits_2 |= 1 << p22; digits_2 |= 1 << p23; digits_2 |= 1 << p24; /* Check that first and second partial products, hence all partial products, * are made up of the same digits. */ if (digits_1 != digits_2) continue; printf("%6d\n x%4d\n", m, n); printf(" ---\n"); printf("%6d\n%5d\n%4d\n", partial_product1, partial_product2, partial_product3); printf("------\n"); printf("%d\n", product); } return EXIT_SUCCESS; }