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from itertools import product
 
# 定义目标数字（可根据需要修改）
TARGET = 272850
 
def find_solutions():
    a_values =  [35, 40.5, 58, 67, 73, 90.5]
    solutions_by_pair = {}
 
    total_iterations = len(a_values) ** 2 * 10000
    print(f"总计算次数: {total_iterations:,}")
 
    count = 0
    for a, b in product(a_values, repeat=2):
        min_x = 1
        max_x = int((TARGET - 1) // a)
 
        if max_x < min_x:
            continue
 
        all_solutions = []  # 存储所有解
        for x in range(min_x, max_x + 1):
            numerator = TARGET - a * x
            if numerator <= 0:
                continue
 
            y = numerator / b
            if y.is_integer() and 1 <= y <= 10000:
                all_solutions.append((x, int(y)))
 
            count += 1
            if count % 1000000 == 0:
                progress = count / total_iterations * 100
                print(f"进度: {progress:.2f}%")
 
        if all_solutions:
            # 按平衡度排序，取前2个平衡解
            balanced_solutions = sorted(all_solutions, key=lambda p: abs(p[0] - p[1]))[:2]
 
            # 从原始解中排除已在平衡解中的项，取前3个
            remaining_solutions = [s for s in all_solutions if s not in balanced_solutions][:3]
 
            # 合并：先2个平衡解，再3个原始解
            combined = balanced_solutions + remaining_solutions
 
            solutions_by_pair[(a, b)] = combined
 
    return solutions_by_pair
 
def display_solutions(solutions_by_pair):
    total_pairs = len(solutions_by_pair)
    print(f"共找到 {total_pairs} 组有效(a, b)组合，目标值为 {TARGET}")
 
    if total_pairs == 0:
        return
 
    sorted_pairs = sorted(solutions_by_pair.keys(), key=lambda x: (x[0], x[1]))
 
    for i, (a, b) in enumerate(sorted_pairs, 1):
        solutions = solutions_by_pair[(a, b)]
        print(f"\n{i}. 组合 a={a}, b={b}: {len(solutions)} 个解")
 
        for j, (x, y) in enumerate(solutions, 1):
            diff = abs(x - y)
            ax = a * x
            by = b * y
            tag = "[平衡解]" if j <= 2 else "[原始解]"
            print(f"   {j}. x={x}, y={y}  (差值: {diff}, a*x={ax}, b*y={by}, a*x + b*y = {ax + by:.1f}) {tag}")
 
if __name__ == "__main__":
    import time
    start_time = time.time()
 
    solutions_by_pair = find_solutions()
    display_solutions(solutions_by_pair)
 
    print(f"计算耗时: {time.time() - start_time:.2f}秒")

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Success #stdin #stdout 0.09s 9572KB

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Standard input is empty

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总计算次数: 360,000
共找到 30 组有效(a, b)组合，目标值为 272850

1. 组合 a=35, b=40.5: 5 个解
   1. x=3630, y=3600  (差值: 30, a*x=127050, b*y=145800.0, a*x + b*y = 272850.0) [平衡解]
   2. x=3549, y=3670  (差值: 121, a*x=124215, b*y=148635.0, a*x + b*y = 272850.0) [平衡解]
   3. x=66, y=6680  (差值: 6614, a*x=2310, b*y=270540.0, a*x + b*y = 272850.0) [原始解]
   4. x=147, y=6610  (差值: 6463, a*x=5145, b*y=267705.0, a*x + b*y = 272850.0) [原始解]
   5. x=228, y=6540  (差值: 6312, a*x=7980, b*y=264870.0, a*x + b*y = 272850.0) [原始解]

2. 组合 a=35, b=58: 5 个解
   1. x=2932, y=2935  (差值: 3, a*x=102620, b*y=170230, a*x + b*y = 272850.0) [平衡解]
   2. x=2990, y=2900  (差值: 90, a*x=104650, b*y=168200, a*x + b*y = 272850.0) [平衡解]
   3. x=32, y=4685  (差值: 4653, a*x=1120, b*y=271730, a*x + b*y = 272850.0) [原始解]
   4. x=90, y=4650  (差值: 4560, a*x=3150, b*y=269700, a*x + b*y = 272850.0) [原始解]
   5. x=148, y=4615  (差值: 4467, a*x=5180, b*y=267670, a*x + b*y = 272850.0) [原始解]

3. 组合 a=35, b=67: 5 个解
   1. x=2675, y=2675  (差值: 0, a*x=93625, b*y=179225, a*x + b*y = 272850.0) [平衡解]
   2. x=2608, y=2710  (差值: 102, a*x=91280, b*y=181570, a*x + b*y = 272850.0) [平衡解]
   3. x=62, y=4040  (差值: 3978, a*x=2170, b*y=270680, a*x + b*y = 272850.0) [原始解]
   4. x=129, y=4005  (差值: 3876, a*x=4515, b*y=268335, a*x + b*y = 272850.0) [原始解]
   5. x=196, y=3970  (差值: 3774, a*x=6860, b*y=265990, a*x + b*y = 272850.0) [原始解]

4. 组合 a=35, b=73: 5 个解
   1. x=2498, y=2540  (差值: 42, a*x=87430, b*y=185420, a*x + b*y = 272850.0) [平衡解]
   2. x=2571, y=2505  (差值: 66, a*x=89985, b*y=182865, a*x + b*y = 272850.0) [平衡解]
   3. x=16, y=3730  (差值: 3714, a*x=560, b*y=272290, a*x + b*y = 272850.0) [原始解]
   4. x=89, y=3695  (差值: 3606, a*x=3115, b*y=269735, a*x + b*y = 272850.0) [原始解]
   5. x=162, y=3660  (差值: 3498, a*x=5670, b*y=267180, a*x + b*y = 272850.0) [原始解]

5. 组合 a=35, b=90.5: 5 个解
   1. x=2133, y=2190  (差值: 57, a*x=74655, b*y=198195.0, a*x + b*y = 272850.0) [平衡解]
   2. x=2314, y=2120  (差值: 194, a*x=80990, b*y=191860.0, a*x + b*y = 272850.0) [平衡解]
   3. x=142, y=2960  (差值: 2818, a*x=4970, b*y=267880.0, a*x + b*y = 272850.0) [原始解]
   4. x=323, y=2890  (差值: 2567, a*x=11305, b*y=261545.0, a*x + b*y = 272850.0) [原始解]
   5. x=504, y=2820  (差值: 2316, a*x=17640, b*y=255210.0, a*x + b*y = 272850.0) [原始解]

6. 组合 a=40.5, b=35: 5 个解
   1. x=3600, y=3630  (差值: 30, a*x=145800.0, b*y=127050, a*x + b*y = 272850.0) [平衡解]
   2. x=3670, y=3549  (差值: 121, a*x=148635.0, b*y=124215, a*x + b*y = 272850.0) [平衡解]
   3. x=30, y=7761  (差值: 7731, a*x=1215.0, b*y=271635, a*x + b*y = 272850.0) [原始解]
   4. x=100, y=7680  (差值: 7580, a*x=4050.0, b*y=268800, a*x + b*y = 272850.0) [原始解]
   5. x=170, y=7599  (差值: 7429, a*x=6885.0, b*y=265965, a*x + b*y = 272850.0) [原始解]

7. 组合 a=40.5, b=58: 5 个解
   1. x=2720, y=2805  (差值: 85, a*x=110160.0, b*y=162690, a*x + b*y = 272850.0) [平衡解]
   2. x=2836, y=2724  (差值: 112, a*x=114858.0, b*y=157992, a*x + b*y = 272850.0) [平衡解]
   3. x=52, y=4668  (差值: 4616, a*x=2106.0, b*y=270744, a*x + b*y = 272850.0) [原始解]
   4. x=168, y=4587  (差值: 4419, a*x=6804.0, b*y=266046, a*x + b*y = 272850.0) [原始解]
   5. x=284, y=4506  (差值: 4222, a*x=11502.0, b*y=261348, a*x + b*y = 272850.0) [原始解]

8. 组合 a=40.5, b=67: 5 个解
   1. x=2588, y=2508  (差值: 80, a*x=104814.0, b*y=168036, a*x + b*y = 272850.0) [平衡解]
   2. x=2454, y=2589  (差值: 135, a*x=99387.0, b*y=173463, a*x + b*y = 272850.0) [平衡解]
   3. x=42, y=4047  (差值: 4005, a*x=1701.0, b*y=271149, a*x + b*y = 272850.0) [原始解]
   4. x=176, y=3966  (差值: 3790, a*x=7128.0, b*y=265722, a*x + b*y = 272850.0) [原始解]
   5. x=310, y=3885  (差值: 3575, a*x=12555.0, b*y=260295, a*x + b*y = 272850.0) [原始解]

9. 组合 a=40.5, b=73: 5 个解
   1. x=2476, y=2364  (差值: 112, a*x=100278.0, b*y=172572, a*x + b*y = 272850.0) [平衡解]
   2. x=2330, y=2445  (差值: 115, a*x=94365.0, b*y=178485, a*x + b*y = 272850.0) [平衡解]
   3. x=140, y=3660  (差值: 3520, a*x=5670.0, b*y=267180, a*x + b*y = 272850.0) [原始解]
   4. x=286, y=3579  (差值: 3293, a*x=11583.0, b*y=261267, a*x + b*y = 272850.0) [原始解]
   5. x=432, y=3498  (差值: 3066, a*x=17496.0, b*y=255354, a*x + b*y = 272850.0) [原始解]

10. 组合 a=40.5, b=90.5: 5 个解
   1. x=2145, y=2055  (差值: 90, a*x=86872.5, b*y=185977.5, a*x + b*y = 272850.0) [平衡解]
   2. x=1964, y=2136  (差值: 172, a*x=79542.0, b*y=193308.0, a*x + b*y = 272850.0) [平衡解]
   3. x=154, y=2946  (差值: 2792, a*x=6237.0, b*y=266613.0, a*x + b*y = 272850.0) [原始解]
   4. x=335, y=2865  (差值: 2530, a*x=13567.5, b*y=259282.5, a*x + b*y = 272850.0) [原始解]
   5. x=516, y=2784  (差值: 2268, a*x=20898.0, b*y=251952.0, a*x + b*y = 272850.0) [原始解]

11. 组合 a=58, b=35: 5 个解
   1. x=2935, y=2932  (差值: 3, a*x=170230, b*y=102620, a*x + b*y = 272850.0) [平衡解]
   2. x=2900, y=2990  (差值: 90, a*x=168200, b*y=104650, a*x + b*y = 272850.0) [平衡解]
   3. x=30, y=7746  (差值: 7716, a*x=1740, b*y=271110, a*x + b*y = 272850.0) [原始解]
   4. x=65, y=7688  (差值: 7623, a*x=3770, b*y=269080, a*x + b*y = 272850.0) [原始解]
   5. x=100, y=7630  (差值: 7530, a*x=5800, b*y=267050, a*x + b*y = 272850.0) [原始解]

12. 组合 a=58, b=40.5: 5 个解
   1. x=2805, y=2720  (差值: 85, a*x=162690, b*y=110160.0, a*x + b*y = 272850.0) [平衡解]
   2. x=2724, y=2836  (差值: 112, a*x=157992, b*y=114858.0, a*x + b*y = 272850.0) [平衡解]
   3. x=51, y=6664  (差值: 6613, a*x=2958, b*y=269892.0, a*x + b*y = 272850.0) [原始解]
   4. x=132, y=6548  (差值: 6416, a*x=7656, b*y=265194.0, a*x + b*y = 272850.0) [原始解]
   5. x=213, y=6432  (差值: 6219, a*x=12354, b*y=260496.0, a*x + b*y = 272850.0) [原始解]

13. 组合 a=58, b=67: 5 个解
   1. x=2156, y=2206  (差值: 50, a*x=125048, b*y=147802, a*x + b*y = 272850.0) [平衡解]
   2. x=2223, y=2148  (差值: 75, a*x=128934, b*y=143916, a*x + b*y = 272850.0) [平衡解]
   3. x=12, y=4062  (差值: 4050, a*x=696, b*y=272154, a*x + b*y = 272850.0) [原始解]
   4. x=79, y=4004  (差值: 3925, a*x=4582, b*y=268268, a*x + b*y = 272850.0) [原始解]
   5. x=146, y=3946  (差值: 3800, a*x=8468, b*y=264382, a*x + b*y = 272850.0) [原始解]

14. 组合 a=58, b=73: 5 个解
   1. x=2104, y=2066  (差值: 38, a*x=122032, b*y=150818, a*x + b*y = 272850.0) [平衡解]
   2. x=2031, y=2124  (差值: 93, a*x=117798, b*y=155052, a*x + b*y = 272850.0) [平衡解]
   3. x=60, y=3690  (差值: 3630, a*x=3480, b*y=269370, a*x + b*y = 272850.0) [原始解]
   4. x=133, y=3632  (差值: 3499, a*x=7714, b*y=265136, a*x + b*y = 272850.0) [原始解]
   5. x=206, y=3574  (差值: 3368, a*x=11948, b*y=260902, a*x + b*y = 272850.0) [原始解]

15. 组合 a=58, b=90.5: 5 个解
   1. x=1852, y=1828  (差值: 24, a*x=107416, b*y=165434.0, a*x + b*y = 272850.0) [平衡解]
   2. x=1671, y=1944  (差值: 273, a*x=96918, b*y=175932.0, a*x + b*y = 272850.0) [平衡解]
   3. x=42, y=2988  (差值: 2946, a*x=2436, b*y=270414.0, a*x + b*y = 272850.0) [原始解]
   4. x=223, y=2872  (差值: 2649, a*x=12934, b*y=259916.0, a*x + b*y = 272850.0) [原始解]
   5. x=404, y=2756  (差值: 2352, a*x=23432, b*y=249418.0, a*x + b*y = 272850.0) [原始解]

16. 组合 a=67, b=35: 5 个解
   1. x=2675, y=2675  (差值: 0, a*x=179225, b*y=93625, a*x + b*y = 272850.0) [平衡解]
   2. x=2640, y=2742  (差值: 102, a*x=176880, b*y=95970, a*x + b*y = 272850.0) [平衡解]
   3. x=15, y=7767  (差值: 7752, a*x=1005, b*y=271845, a*x + b*y = 272850.0) [原始解]
   4. x=50, y=7700  (差值: 7650, a*x=3350, b*y=269500, a*x + b*y = 272850.0) [原始解]
   5. x=85, y=7633  (差值: 7548, a*x=5695, b*y=267155, a*x + b*y = 272850.0) [原始解]

17. 组合 a=67, b=40.5: 5 个解
   1. x=2508, y=2588  (差值: 80, a*x=168036, b*y=104814.0, a*x + b*y = 272850.0) [平衡解]
   2. x=2589, y=2454  (差值: 135, a*x=173463, b*y=99387.0, a*x + b*y = 272850.0) [平衡解]
   3. x=78, y=6608  (差值: 6530, a*x=5226, b*y=267624.0, a*x + b*y = 272850.0) [原始解]
   4. x=159, y=6474  (差值: 6315, a*x=10653, b*y=262197.0, a*x + b*y = 272850.0) [原始解]
   5. x=240, y=6340  (差值: 6100, a*x=16080, b*y=256770.0, a*x + b*y = 272850.0) [原始解]

18. 组合 a=67, b=58: 5 个解
   1. x=2206, y=2156  (差值: 50, a*x=147802, b*y=125048, a*x + b*y = 272850.0) [平衡解]
   2. x=2148, y=2223  (差值: 75, a*x=143916, b*y=128934, a*x + b*y = 272850.0) [平衡解]
   3. x=2, y=4702  (差值: 4700, a*x=134, b*y=272716, a*x + b*y = 272850.0) [原始解]
   4. x=60, y=4635  (差值: 4575, a*x=4020, b*y=268830, a*x + b*y = 272850.0) [原始解]
   5. x=118, y=4568  (差值: 4450, a*x=7906, b*y=264944, a*x + b*y = 272850.0) [原始解]

19. 组合 a=67, b=73: 5 个解
   1. x=1975, y=1925  (差值: 50, a*x=132325, b*y=140525, a*x + b*y = 272850.0) [平衡解]
   2. x=1902, y=1992  (差值: 90, a*x=127434, b*y=145416, a*x + b*y = 272850.0) [平衡解]
   3. x=4, y=3734  (差值: 3730, a*x=268, b*y=272582, a*x + b*y = 272850.0) [原始解]
   4. x=77, y=3667  (差值: 3590, a*x=5159, b*y=267691, a*x + b*y = 272850.0) [原始解]
   5. x=150, y=3600  (差值: 3450, a*x=10050, b*y=262800, a*x + b*y = 272850.0) [原始解]

20. 组合 a=67, b=90.5: 5 个解
   1. x=1741, y=1726  (差值: 15, a*x=116647, b*y=156203.0, a*x + b*y = 272850.0) [平衡解]
   2. x=1560, y=1860  (差值: 300, a*x=104520, b*y=168330.0, a*x + b*y = 272850.0) [平衡解]
   3. x=112, y=2932  (差值: 2820, a*x=7504, b*y=265346.0, a*x + b*y = 272850.0) [原始解]
   4. x=293, y=2798  (差值: 2505, a*x=19631, b*y=253219.0, a*x + b*y = 272850.0) [原始解]
   5. x=474, y=2664  (差值: 2190, a*x=31758, b*y=241092.0, a*x + b*y = 272850.0) [原始解]

21. 组合 a=73, b=35: 5 个解
   1. x=2540, y=2498  (差值: 42, a*x=185420, b*y=87430, a*x + b*y = 272850.0) [平衡解]
   2. x=2505, y=2571  (差值: 66, a*x=182865, b*y=89985, a*x + b*y = 272850.0) [平衡解]
   3. x=20, y=7754  (差值: 7734, a*x=1460, b*y=271390, a*x + b*y = 272850.0) [原始解]
   4. x=55, y=7681  (差值: 7626, a*x=4015, b*y=268835, a*x + b*y = 272850.0) [原始解]
   5. x=90, y=7608  (差值: 7518, a*x=6570, b*y=266280, a*x + b*y = 272850.0) [原始解]

22. 组合 a=73, b=40.5: 5 个解
   1. x=2364, y=2476  (差值: 112, a*x=172572, b*y=100278.0, a*x + b*y = 272850.0) [平衡解]
   2. x=2445, y=2330  (差值: 115, a*x=178485, b*y=94365.0, a*x + b*y = 272850.0) [平衡解]
   3. x=15, y=6710  (差值: 6695, a*x=1095, b*y=271755.0, a*x + b*y = 272850.0) [原始解]
   4. x=96, y=6564  (差值: 6468, a*x=7008, b*y=265842.0, a*x + b*y = 272850.0) [原始解]
   5. x=177, y=6418  (差值: 6241, a*x=12921, b*y=259929.0, a*x + b*y = 272850.0) [原始解]

23. 组合 a=73, b=58: 5 个解
   1. x=2066, y=2104  (差值: 38, a*x=150818, b*y=122032, a*x + b*y = 272850.0) [平衡解]
   2. x=2124, y=2031  (差值: 93, a*x=155052, b*y=117798, a*x + b*y = 272850.0) [平衡解]
   3. x=36, y=4659  (差值: 4623, a*x=2628, b*y=270222, a*x + b*y = 272850.0) [原始解]
   4. x=94, y=4586  (差值: 4492, a*x=6862, b*y=265988, a*x + b*y = 272850.0) [原始解]
   5. x=152, y=4513  (差值: 4361, a*x=11096, b*y=261754, a*x + b*y = 272850.0) [原始解]

24. 组合 a=73, b=67: 5 个解
   1. x=1925, y=1975  (差值: 50, a*x=140525, b*y=132325, a*x + b*y = 272850.0) [平衡解]
   2. x=1992, y=1902  (差值: 90, a*x=145416, b*y=127434, a*x + b*y = 272850.0) [平衡解]
   3. x=49, y=4019  (差值: 3970, a*x=3577, b*y=269273, a*x + b*y = 272850.0) [原始解]
   4. x=116, y=3946  (差值: 3830, a*x=8468, b*y=264382, a*x + b*y = 272850.0) [原始解]
   5. x=183, y=3873  (差值: 3690, a*x=13359, b*y=259491, a*x + b*y = 272850.0) [原始解]

25. 组合 a=73, b=90.5: 5 个解
   1. x=1707, y=1638  (差值: 69, a*x=124611, b*y=148239.0, a*x + b*y = 272850.0) [平衡解]
   2. x=1526, y=1784  (差值: 258, a*x=111398, b*y=161452.0, a*x + b*y = 272850.0) [平衡解]
   3. x=78, y=2952  (差值: 2874, a*x=5694, b*y=267156.0, a*x + b*y = 272850.0) [原始解]
   4. x=259, y=2806  (差值: 2547, a*x=18907, b*y=253943.0, a*x + b*y = 272850.0) [原始解]
   5. x=440, y=2660  (差值: 2220, a*x=32120, b*y=240730.0, a*x + b*y = 272850.0) [原始解]

26. 组合 a=90.5, b=35: 5 个解
   1. x=2190, y=2133  (差值: 57, a*x=198195.0, b*y=74655, a*x + b*y = 272850.0) [平衡解]
   2. x=2120, y=2314  (差值: 194, a*x=191860.0, b*y=80990, a*x + b*y = 272850.0) [平衡解]
   3. x=20, y=7744  (差值: 7724, a*x=1810.0, b*y=271040, a*x + b*y = 272850.0) [原始解]
   4. x=90, y=7563  (差值: 7473, a*x=8145.0, b*y=264705, a*x + b*y = 272850.0) [原始解]
   5. x=160, y=7382  (差值: 7222, a*x=14480.0, b*y=258370, a*x + b*y = 272850.0) [原始解]

27. 组合 a=90.5, b=40.5: 5 个解
   1. x=2055, y=2145  (差值: 90, a*x=185977.5, b*y=86872.5, a*x + b*y = 272850.0) [平衡解]
   2. x=2136, y=1964  (差值: 172, a*x=193308.0, b*y=79542.0, a*x + b*y = 272850.0) [平衡解]
   3. x=30, y=6670  (差值: 6640, a*x=2715.0, b*y=270135.0, a*x + b*y = 272850.0) [原始解]
   4. x=111, y=6489  (差值: 6378, a*x=10045.5, b*y=262804.5, a*x + b*y = 272850.0) [原始解]
   5. x=192, y=6308  (差值: 6116, a*x=17376.0, b*y=255474.0, a*x + b*y = 272850.0) [原始解]

28. 组合 a=90.5, b=58: 5 个解
   1. x=1828, y=1852  (差值: 24, a*x=165434.0, b*y=107416, a*x + b*y = 272850.0) [平衡解]
   2. x=1944, y=1671  (差值: 273, a*x=175932.0, b*y=96918, a*x + b*y = 272850.0) [平衡解]
   3. x=88, y=4567  (差值: 4479, a*x=7964.0, b*y=264886, a*x + b*y = 272850.0) [原始解]
   4. x=204, y=4386  (差值: 4182, a*x=18462.0, b*y=254388, a*x + b*y = 272850.0) [原始解]
   5. x=320, y=4205  (差值: 3885, a*x=28960.0, b*y=243890, a*x + b*y = 272850.0) [原始解]

29. 组合 a=90.5, b=67: 5 个解
   1. x=1726, y=1741  (差值: 15, a*x=156203.0, b*y=116647, a*x + b*y = 272850.0) [平衡解]
   2. x=1860, y=1560  (差值: 300, a*x=168330.0, b*y=104520, a*x + b*y = 272850.0) [平衡解]
   3. x=118, y=3913  (差值: 3795, a*x=10679.0, b*y=262171, a*x + b*y = 272850.0) [原始解]
   4. x=252, y=3732  (差值: 3480, a*x=22806.0, b*y=250044, a*x + b*y = 272850.0) [原始解]
   5. x=386, y=3551  (差值: 3165, a*x=34933.0, b*y=237917, a*x + b*y = 272850.0) [原始解]

30. 组合 a=90.5, b=73: 5 个解
   1. x=1638, y=1707  (差值: 69, a*x=148239.0, b*y=124611, a*x + b*y = 272850.0) [平衡解]
   2. x=1784, y=1526  (差值: 258, a*x=161452.0, b*y=111398, a*x + b*y = 272850.0) [平衡解]
   3. x=32, y=3698  (差值: 3666, a*x=2896.0, b*y=269954, a*x + b*y = 272850.0) [原始解]
   4. x=178, y=3517  (差值: 3339, a*x=16109.0, b*y=256741, a*x + b*y = 272850.0) [原始解]
   5. x=324, y=3336  (差值: 3012, a*x=29322.0, b*y=243528, a*x + b*y = 272850.0) [原始解]
计算耗时: 0.06秒

https://ideone.com/44R6nR

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Python 3 nbc (python 3.7.3)

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