程序代码：

#include <stdio.h>

void Swap(int* p1, int* p2)
{
    int tmp = *p1; *p1 = *p2; *p2 = tmp;
}

void Reverse(int* start, int* end)
{
    while (start < end)
        Swap(start++, --end);
}

int NextPermutation(int* start, int* end)
{
    int* p, *sp = end - 2;
    if (start >= end - 1)
        return 0;
    while (sp >= start) {
        if (sp[0] < sp[1])
            break;
        --sp;
    }
    if (sp < start) {
        Reverse(start, end);
        return 0;
    }
    for (p = end - 1; p > sp; --p)
        if (*p > *sp) {
            Swap(sp, p);
            break;
        }
    Reverse(sp + 1, end);
    return 1;
}

/*

 * X1/(X2*10+X3) + X4/(X5*10+X6) + X7/(X8*10+X9) = 1

 *<==>

 * X1*(X5*10+X6)*(X8*10+X9) + X4*(X2*10+X3)*(X8*10+X9) + X7*(X2*10+X3)*(X5*10+X6) = (X2*10+X3)*(X5*10+X6)*(X8*10+X9)

 */

int main()
{
    int x[] = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
    do {
        if (x[0] * (x[4] * 10 + x[5]) * (x[7] * 10 + x[8]) +
            x[3] * (x[1] * 10 + x[2]) * (x[7] * 10 + x[8]) +
            x[6] * (x[1] * 10 + x[2]) * (x[4] * 10 + x[5]) == (x[1] * 10 + x[2]) * (x[4] * 10 + x[5]) * (x[7] * 10 + x[8]))
        {
            printf("%4d%10d%10d\n", x[0], x[3], x[6]);
            printf("------- + ------- + ------- = 1\n");
            printf("%4d%10d%10d\n\n", x[1] * 10 + x[2], x[4] * 10 + x[5], x[7] * 10 + x[8]);
        }
    } while (NextPermutation(x, x + 9));
    return 0;
}