参考程序代码：

#include <iostream>
#include <vector>

int main() {
    // 小球的重量
    std::vector<int> weights = {1, 2, 3, 4, 5};
    
    // 用来存储可能的结果
    int a, b, c, d, e, x;

    // 穷举所有可能的 a, b, c, d, e 的组合
    for (int i = 0; i < weights.size(); ++i) {
        for (int j = 0; j < weights.size(); ++j) {
            if (j == i) continue; // 确保不同的小球
            for (int k = 0; k < weights.size(); ++k) {
                if (k == i || k == j) continue;
                for (int l = 0; l < weights.size(); ++l) {
                    if (l == i || l == j || l == k) continue;
                    for (int m = 0; m < weights.size(); ++m) {
                        if (m == i || m == j || m == k || m == l) continue;

                        // 分别赋值
                        a = weights[i];
                        b = weights[j];
                        c = weights[k];
                        d = weights[l];
                        e = weights[m];

                        // 计算 x 的值
                        // x + a = b + c  ==>  x = b + c - a
                        x = b + c - a;

                        // 验证 x 是否有效并且在范围内
                        if (x > 0 ) {
                            // 验证其他方程
                            if (x + b == a + c + d + e && x + d == c + e) {
                                // 输出结果
                                std::cout << "a: " << a << ", b: " << b << ", c: " << c 
                                          << ", d: " << d << ", e: " << e << ", x: " << x << std::endl;
                            }
                        }
                    }
                }
            }
        }
    }

    return 0;
}