这是一篇写在它处的老文章了。近日翻翻,颇有意思。于是在此再次发布。
研究24点的算法。觉得穷举法是一种可以接受的解法。利用时下的计算机。就是穷举从1,1,1,1到10,10,10,10的所有数字组合的解法也不过就几秒钟而已。而且,可以将所有的结果保存在文件里,以供日后其他应用时方便调用,加快计算速度。下面将有结果的组合和解法赋予其后,有兴趣的同道之人可以参阅。
1,1,1,8 --- 8×(1+1+1)=24
1,1,2,6 --- 2×6×(1+1)=24
1,1,2,7 --- (1+2)×(7+1)=24
1,1,2,8 --- (1+2)×8×1=24
1,1,2,9 --- (1+2)×(9-1)=24
1,1,2,10 --- 2×(1+10+1)=24
1,1,3,4 --- 3×4×(1+1)=24
1,1,3,5 --- (1+3)×(5+1)=24
1,1,3,6 --- (1+3)×6×1=24
1,1,3,7 --- (1+3)×(7-1)=24
1,1,3,8 --- 1+3×8-1=24
1,1,3,9 --- 1×3×(9-1)=24
1,1,3,10 --- 3×(10-1-1)=24
1,1,4,4 --- 4×(1+4+1)=24
1,1,4,5 --- (1+4)×5-1=24
1,1,4,6 --- 1+4×6-1=24
1,1,4,7 --- 1×4×(7-1)=24
1,1,4,8 --- (4-1)×8×1=24
1,1,4,9 --- (4-1)×(9-1)=24
1,1,4,10 --- 4+10×(1+1)=24
1,1,5,5 --- (1+5)×(5-1)=24
1,1,5,6 --- (5-1)×6×1=24
1,1,5,7 --- (5-1)×(7-1)=24
1,1,5,8 --- 8×(5-1-1)=24
1,1,6,6 --- (6+6)×(1+1)=24
1,1,6,8 --- 6×8÷(1+1)=24
1,1,6,9 --- 6+9×(1+1)=24
1,1,7,10 --- 10+7×(1+1)=24
1,1,8,8 --- 8+8×(1+1)=24
1,2,2,4 --- 2×4×(2+1)=24
1,2,2,5 --- (2+2)×(5+1)=24
1,2,2,6 --- (2+2)×6×1=24
1,2,2,7 --- (2+2)×(7-1)=24
1,2,2,8 --- 8×(2+2-1)=24
1,2,2,9 --- 2×(2+9+1)=24
1,2,2,10 --- 2+2×(10+1)=24
1,2,3,3 --- 2×3×(3+1)=24
1,2,3,4 --- 2×3×4×1=24
1,2,3,5 --- (2+3)×5-1=24
1,2,3,6 --- 3×(2+6)×1=24
1,2,3,7 --- 2+3×7+1=24
1,2,3,8 --- 2×(3+8+1)=24
1,2,3,9 --- 2×(3+9)×1=24
1,2,3,10 --- 2×(3+10-1)=24
1,2,4,4 --- (2+4)×4×1=24
1,2,4,5 --- (2+4)×(5-1)=24
1,2,4,6 --- 4×6×(2-1)=24
1,2,4,7 --- 2×(4+7+1)=24
1,2,4,8 --- 2×(4+8)×1=24
1,2,4,9 --- 2×(4+9-1)=24
1,2,4,10 --- 4+2×10×1=24
1,2,5,5 --- 5×5-2+1=24
1,2,5,6 --- 2×(5+6+1)=24
1,2,5,7 --- 2×(5+7)×1=24
1,2,5,8 --- 2×(5+8-1)=24
1,2,5,9 --- 5+2×9+1=24
1,2,5,10 --- 5+2×10-1=24
1,2,6,6 --- 2×(6+6)×1=24
1,2,6,7 --- 2×(6+7-1)=24
1,2,6,8 --- 6+2×(8+1)=24
1,2,6,9 --- 6+2×9×1=24
1,2,6,10 --- 6+2×(10-1)=24
1,2,7,7 --- (7×7-1)÷2=24
1,2,7,8 --- 7+2×8+1=24
1,2,7,9 --- 2×7+9+1=24
1,2,7,10 --- 2×7+10×1=24
1,2,8,8 --- 2×8+8×1=24
1,2,8,9 --- 2×8+9-1=24
1,2,8,10 --- 10+2×(8-1)=24
1,3,3,3 --- (3+3)×(3+1)=24
1,3,3,4 --- (3+3)×4×1=24
1,3,3,5 --- (3+3)×(5-1)=24
1,3,3,6 --- 3+3×(6+1)=24
1,3,3,7 --- 3+3×7×1=24
1,3,3,8 --- 3+3×(8-1)=24
1,3,3,9 --- (3+9)×(3-1)=24
1,3,3,10 --- 3×(10-3+1)=24
1,3,4,4 --- 3×(4+4)×1=24
1,3,4,5 --- 3+4×5+1=24
1,3,4,6 --- 6÷(1-3÷4)=24
1,3,4,7 --- 4+3×7-1=24
1,3,4,8 --- (4+8)×(3-1)=24
1,3,4,9 --- 4×(9-3)×1=24
1,3,4,10 --- 4+10×(3-1)=24
1,3,5,6 --- 5+3×6+1=24
1,3,5,7 --- (5+7)×(3-1)=24
1,3,5,8 --- 3×5+8+1=24
1,3,5,9 --- 3×5+9×1=24
1,3,5,10 --- 3×5+10-1=24
1,3,6,6 --- 3×6+6×1=24
1,3,6,7 --- 3×6+7-1=24
1,3,6,8 --- (6-3)×8×1=24
1,3,6,9 --- (6-3)×(9-1)=24
1,3,6,10 --- 3×10-6×1=24
1,3,7,7 --- (7-3)×(7-1)=24
1,3,7,8 --- 8×(7-3-1)=24
1,3,7,9 --- 9÷3×(7+1)=24
1,3,7,10 --- 10+7×(3-1)=24
1,3,8,8 --- 8÷3×(8+1)=24
1,3,8,9 --- 8÷3×9×1=24
1,3,8,10 --- 8÷3×(10-1)=24
1,3,9,9 --- 9÷3×(9-1)=24
1,3,9,10 --- 3×(10+1)-9=24
1,3,10,10 --- 3+10+10+1=24
1,4,4,4 --- 4+4×(4+1)=24
1,4,4,5 --- 4+4×5×1=24
1,4,4,6 --- 4+4×(6-1)=24
1,4,4,7 --- 4×4+7+1=24
1,4,4,8 --- 4×4+8×1=24
1,4,4,9 --- 4×4+9-1=24
1,4,4,10 --- 4×(10-4)×1=24
1,4,5,5 --- 4+5×(5-1)=24
1,4,5,6 --- 6÷(5÷4-1)=24
1,4,5,7 --- 4×7-5+1=24
1,4,5,8 --- 8+4×(5-1)=24
1,4,5,9 --- 5×(9-4)-1=24
1,4,5,10 --- 4×(10-5+1)=24
1,4,6,6 --- 6+6×(4-1)=24
1,4,6,7 --- 6×(7-4+1)=24
1,4,6,8 --- 6×(8-4)×1=24
1,4,6,9 --- 6×(9-4-1)=24
1,4,6,10 --- 10×(4-1)-6=24
1,4,7,7 --- (7-4)×(7+1)=24
1,4,7,8 --- (7-4)×8×1=24
1,4,7,9 --- (7-4)×(9-1)=24
1,4,8,8 --- 4×8-8×1=24
1,4,8,9 --- 4×8-9+1=24
1,4,9,10 --- 4+9+10+1=24
1,4,10,10 --- 4+10+10×1=24
1,5,5,5 --- 5×(5-1÷5)=24
1,5,5,6 --- 5×6-5-1=24
1,5,5,9 --- (9-5)×(5+1)=24
1,5,5,10 --- 5×(10-5)-1=24
1,5,6,6 --- 5×6-6×1=24
1,5,6,7 --- 5×6-7+1=24
1,5,6,8 --- 6×(8-5+1)=24
1,5,6,9 --- 6×(9-5)×1=24
1,5,6,10 --- 6×(10-5-1)=24
1,5,7,8 --- 8×(7-5+1)=24
1,5,7,9 --- (9-5)×(7-1)=24
1,5,7,10 --- 5×7-10-1=24
1,5,8,8 --- (8-5)×8×1=24
1,5,8,9 --- (8-5)×(9-1)=24
1,5,8,10 --- 5+8+10+1=24
1,5,9,9 --- 5+9+9+1=24
1,5,9,10 --- 5+9+10×1=24
1,5,10,10 --- 5+10+10-1=24
1,6,6,6 --- 6×(6-1)-6=24
1,6,6,8 --- 6÷(1-6÷8)=24
1,6,6,9 --- 6×(9-6+1)=24
1,6,6,10 --- 6×(10-6)×1=24
1,6,7,9 --- (9-6)×(7+1)=24
1,6,7,10 --- 6+7+10+1=24
1,6,8,8 --- 8×(8-6+1)=24
1,6,8,9 --- 6+8+9+1=24
1,6,8,10 --- 6+8+10×1=24
1,6,9,9 --- 6+9+9×1=24
1,6,9,10 --- 6+9+10-1=24
1,7,7,9 --- 7+7+9+1=24
1,7,7,10 --- 7+7+10×1=24
1,7,8,8 --- 7+8+8+1=24
1,7,8,9 --- 7+8+9×1=24
1,7,8,10 --- 7+8+10-1=24
1,7,9,9 --- 7+9+9-1=24
1,7,9,10 --- (10-7)×(9-1)=24
1,8,8,8 --- 8+8+8×1=24
1,8,8,9 --- 8+8+9-1=24
1,8,8,10 --- 8×(10-8+1)=24
2,2,2,3 --- (2+2)×3×2=24
2,2,2,4 --- (2+2)×(4+2)=24
2,2,2,5 --- (2+2×5)×2=24
2,2,2,7 --- 2×(2×7-2)=24
2,2,2,8 --- (2+2+8)×2=24
2,2,2,9 --- 2+(2+9)×2=24
2,2,2,10 --- 2+2+10×2=24
2,2,3,3 --- 2×(3+3)×2=24
2,2,3,4 --- 3×(2+4+2)=24
2,2,3,5 --- 3×(2×5-2)=24
2,2,3,6 --- (2×3+6)×2=24
2,2,3,7 --- (2+3+7)×2=24
2,2,3,8 --- 2+(3+8)×2=24
2,2,3,9 --- 2×3+9×2=24
2,2,3,10 --- 2×(3+10)-2=24
2,2,4,4 --- (2×4+4)×2=24
2,2,4,5 --- 2+4×5+2=24
2,2,4,6 --- (2+4+6)×2=24
2,2,4,7 --- 2+(4+7)×2=24
2,2,4,8 --- (2+4)×8÷2=24
2,2,4,9 --- 2+4+9×2=24
2,2,4,10 --- 2×(4+10-2)=24
2,2,5,5 --- (2+5+5)×2=24
2,2,5,6 --- 2+(5+6)×2=24
2,2,5,7 --- 2×5+7×2=24
2,2,5,8 --- 2×(5+8)-2=24
2,2,5,9 --- 2×(5+9-2)=24
2,2,5,10 --- (5-2)×(10-2)=24
2,2,6,6 --- (2+6)×6÷2=24
2,2,6,7 --- 2×(6+7)-2=24
2,2,6,8 --- 2+6+8×2=24
2,2,6,9 --- (6÷2+9)×2=24
2,2,6,10 --- 2×6+10+2=24
2,2,7,7 --- 2×(7+7-2)=24
2,2,7,8 --- 2×7+8+2=24
2,2,7,10 --- 2×(7+10÷2)=24
2,2,8,8 --- 2×(8+8÷2)=24
2,2,8,9 --- 8+2×9-2=24
2,2,8,10 --- 2×8+10-2=24
2,2,9,10 --- 10+(9-2)×2=24
2,2,10,10 --- 2+10+10+2=24
2,3,3,3 --- (3+3×3)×2=24
2,3,3,5 --- 3+3×(5+2)=24
2,3,3,6 --- (3+3+6)×2=24
2,3,3,7 --- 3×(3+7-2)=24
2,3,3,8 --- (3+3)×8÷2=24
2,3,3,9 --- 3+3+9×2=24
2,3,3,10 --- 3×(3+10÷2)=24
2,3,4,4 --- 3×4×(4-2)=24
2,3,4,5 --- (3+4+5)×2=24
2,3,4,6 --- 3×(4+6-2)=24
2,3,4,7 --- 4+(3+7)×2=24
2,3,4,8 --- 3×(4+8÷2)=24
2,3,4,9 --- 4×(3+9)÷2=24
2,3,4,10 --- 3×4+10+2=24
2,3,5,5 --- (3+5)×(5-2)=24
2,3,5,6 --- (3+5)×6÷2=24
2,3,5,7 --- 3×5+7+2=24
2,3,5,8 --- 3+5+8×2=24
2,3,5,9 --- (3+5×9)÷2=24
2,3,5,10 --- (5-3+10)×2=24
2,3,6,6 --- (3×6-6)×2=24
2,3,6,7 --- 3+6×7÷2=24
2,3,6,8 --- 3×6+8-2=24
2,3,6,9 --- (6-3+9)×2=24
2,3,6,10 --- 3×(6+10)÷2=24
2,3,7,7 --- 3+7+7×2=24
2,3,7,8 --- (7-3+8)×2=24
2,3,7,9 --- 3×(7+9)÷2=24
2,3,7,10 --- 7-3+10×2=24
2,3,8,8 --- 3×(8+8)÷2=24
2,3,8,9 --- 8×(9-3×2)=24
2,3,8,10 --- 8+10+3×2=24
2,3,9,9 --- 9-3+9×2=24
2,3,9,10 --- 3+9+10+2=24
2,3,10,10 --- 10-(3-10)×2=24
2,4,4,4 --- (4+4+4)×2=24
2,4,4,5 --- (4+4)×(5-2)=24
2,4,4,6 --- 4+(4+6)×2=24
2,4,4,7 --- 4+4×(7-2)=24
2,4,4,8 --- 4+4+8×2=24
2,4,4,9 --- 4×(9-2)-4=24
2,4,4,10 --- 4+4×10÷2=24
2,4,5,5 --- 4+(5+5)×2=24
2,4,5,6 --- 4+5×(6-2)=24
2,4,5,7 --- 4×(5+7)÷2=24
2,4,5,8 --- 4+5×8÷2=24
2,4,5,9 --- (9-5)×(4+2)=24
2,4,5,10 --- 4+10+5×2=24
2,4,6,6 --- 4×(6+6)÷2=24
2,4,6,7 --- 4+6+7×2=24
2,4,6,8 --- 6÷4×8×2=24
2,4,6,9 --- 6+4×9÷2=24
2,4,6,10 --- (6-4+10)×2=24
2,4,7,7 --- (7+7)×2-4=24
2,4,7,8 --- 4×7-8÷2=24
2,4,7,9 --- (7-4+9)×2=24
2,4,7,10 --- (7-4)×(10-2)=24
2,4,8,8 --- 8+4×8÷2=24
2,4,8,9 --- 8×(9-4-2)=24
2,4,8,10 --- 4+8+10+2=24
2,4,9,9 --- 4+9+9+2=24
2,4,9,10 --- 4×9-10-2=24
2,4,10,10 --- 10×(4÷10+2)=24
2,5,5,7 --- 5+5+7×2=24
2,5,5,8 --- 8×(5÷5+2)=24
2,5,5,9 --- 5+9+5×2=24
2,5,5,10 --- (5-2÷10)×5=24
2,5,6,6 --- 6+6×(5-2)=24
2,5,6,7 --- 6×(7-5+2)=24
2,5,6,8 --- 5×6-8+2=24
2,5,6,9 --- 9+6×5÷2=24
2,5,6,10 --- 6÷5×10×2=24
2,5,7,7 --- 7+7+5×2=24
2,5,7,8 --- 8×(5×2-7)=24
2,5,7,9 --- 5×7-9-2=24
2,5,7,10 --- 5+7+10+2=24
2,5,8,8 --- (5×8+8)÷2=24
2,5,8,9 --- 5+8+9+2=24
2,5,8,10 --- (8-5)×(10-2)=24
2,5,9,10 --- 9-5+10×2=24
2,5,10,10 --- (10÷5+10)×2=24
2,6,6,6 --- 6+6+6×2=24
2,6,6,7 --- (6+6×7)÷2=24
2,6,6,8 --- 6×(8-6+2)=24
2,6,6,9 --- (6×9-6)÷2=24
2,6,6,10 --- 6+6+10+2=24
2,6,7,8 --- 8×(7-6+2)=24
2,6,7,9 --- 6+7+9+2=24
2,6,7,10 --- (10-7)×(6+2)=24
2,6,8,8 --- 6+8+8+2=24
2,6,8,9 --- 8÷6×9×2=24
2,6,8,10 --- (8-6+10)×2=24
2,6,9,9 --- (9-6+9)×2=24
2,6,9,10 --- 6×(9-10÷2)=24
2,6,10,10 --- 6+10+10-2=24
2,7,7,8 --- 7+7+8+2=24
2,7,7,10 --- 7×(10÷7+2)=24
2,7,8,8 --- (7×8-8)÷2=24
2,7,8,9 --- (7+9)×2-8=24
2,7,9,10 --- 7+9+10-2=24
2,7,10,10 --- (10-7)×(10-2)=24
2,8,8,8 --- 8×(8÷8+2)=24
2,8,8,9 --- 8×(9-8+2)=24
2,8,8,10 --- 8+8+10-2=24
2,8,9,9 --- 8+9+9-2=24
2,8,9,10 --- 8×(10-9+2)=24
2,8,10,10 --- 8×(10÷10+2)=24
2,9,10,10 --- 9+10+10÷2=24
3,3,3,3 --- 3×3×3-3=24
3,3,3,4 --- 3+(3+4)×3=24
3,3,3,5 --- 3×3+5×3=24
3,3,3,6 --- 3+3+6×3=24
3,3,3,7 --- (3+3)×(7-3)=24
3,3,3,8 --- 3+3×8-3=24
3,3,3,9 --- 3×(9-3÷3)=24
3,3,3,10 --- 3+3×(10-3)=24
3,3,4,4 --- 3×4+4×3=24
3,3,4,5 --- 3×(4+5)-3=24
3,3,4,6 --- 3+4×6-3=24
3,3,4,7 --- 3×(4+7-3)=24
3,3,4,8 --- (4-3)×8×3=24
3,3,4,9 --- (3-4+9)×3=24
3,3,5,5 --- 5×5-3÷3=24
3,3,5,6 --- (3+5)×(6-3)=24
3,3,5,7 --- (3×5-7)×3=24
3,3,5,9 --- (3+5)×9÷3=24
3,3,5,10 --- (3-5+10)×3=24
3,3,6,6 --- 3×(6+6÷3)=24
3,3,6,7 --- 6+3×7-3=24
3,3,6,8 --- (3+6)×8÷3=24
3,3,6,9 --- 3-6+9×3=24
3,3,6,10 --- (3×6-10)×3=24
3,3,7,7 --- 7×(3÷7+3)=24
3,3,7,8 --- 7+8+3×3=24
3,3,7,9 --- 3+7×9÷3=24
3,3,8,8 --- 8÷(3-8÷3)=24
3,3,8,9 --- 8×(9-3-3)=24
3,3,8,10 --- 3+8+10+3=24
3,3,9,9 --- 3+9+9+3=24
3,3,9,10 --- 3-9+10×3=24
3,4,4,4 --- 4×(4+3)-4=24
3,4,4,5 --- 4×4+5+3=24
3,4,4,6 --- (4+4)×(6-3)=24
3,4,4,7 --- (4÷4+7)×3=24
3,4,4,8 --- 4+4×(8-3)=24
3,4,4,9 --- (4+4)×9÷3=24
3,4,4,10 --- 4×(10-3)-4=24
3,4,5,5 --- 4+5+5×3=24
3,4,5,6 --- 6×(5-4+3)=24
3,4,5,7 --- 4+5×(7-3)=24
3,4,5,8 --- (4+5)×8÷3=24
3,4,5,9 --- (4-5+9)×3=24
3,4,5,10 --- 4÷5×10×3=24
3,4,6,6 --- (6-4+6)×3=24
3,4,6,8 --- 6×(4+8)÷3=24
3,4,6,9 --- (6-4)×(9+3)=24
3,4,6,10 --- 4+6×10÷3=24
3,4,7,7 --- 4×7-7+3=24
3,4,7,8 --- 8+4×(7-3)=24
3,4,7,9 --- 4-7+9×3=24
3,4,7,10 --- 4+7+10+3=24
3,4,8,9 --- 4+8+9+3=24
3,4,8,10 --- 4×(8+10)÷3=24
3,4,9,9 --- 4×(9+9)÷3=24
3,4,10,10 --- 4-10+10×3=24
3,5,5,6 --- 6×(5÷5+3)=24
3,5,5,7 --- (5÷5+7)×3=24
3,5,5,8 --- 5-5+8×3=24
3,5,5,9 --- 5×(9÷5+3)=24
3,5,6,6 --- (6+6)×(5-3)=24
3,5,6,7 --- (6-5+7)×3=24
3,5,6,8 --- (6-5)×8×3=24
3,5,6,9 --- (5-6+9)×3=24
3,5,6,10 --- 5+6+10+3=24
3,5,7,8 --- 5×7-8-3=24
3,5,7,9 --- 5+7+9+3=24
3,5,7,10 --- (5-7+10)×3=24
3,5,8,8 --- 5+8+8+3=24
3,5,8,9 --- 5-8+9×3=24
3,5,9,9 --- 9+5×9÷3=24
3,5,9,10 --- 9-(5-10)×3=24
3,5,10,10 --- (10-10÷5)×3=24
3,6,6,6 --- 6+6×(6-3)=24
3,6,6,7 --- (6÷6+7)×3=24
3,6,6,8 --- 6-6+8×3=24
3,6,6,9 --- 6+6+9+3=24
3,6,6,10 --- 10×(6-3)-6=24
3,6,7,7 --- 6×(7÷7+3)=24
3,6,7,8 --- 6+7+8+3=24
3,6,7,9 --- (6-7+9)×3=24
3,6,7,10 --- 10+7×6÷3=24
3,6,8,8 --- 6×8-8×3=24
3,6,8,9 --- (8-6)×(9+3)=24
3,6,8,10 --- (6-8+10)×3=24
3,6,9,9 --- 6-9+9×3=24
3,6,9,10 --- 6×9-10×3=24
3,6,10,10 --- 6×(10÷10+3)=24
3,7,7,7 --- 7+7+7+3=24
3,7,7,8 --- 7-7+8×3=24
3,7,7,9 --- (9-7÷7)×3=24
3,7,7,10 --- 7×(10-7)+3=24
3,7,8,8 --- (7+8÷8)×3=24
3,7,8,9 --- (7-8+9)×3=24
3,7,9,9 --- (7+9÷9)×3=24
3,7,9,10 --- (7-9+10)×3=24
3,7,10,10 --- 7+10+10-3=24
3,8,8,8 --- (8+8-8)×3=24
3,8,8,9 --- 8×(9-8)×3=24
3,8,8,10 --- (8×10-8)÷3=24
3,8,9,9 --- (8+9-9)×3=24
3,8,9,10 --- 8+9+10-3=24
3,8,10,10 --- (8+10-10)×3=24
3,9,9,9 --- 9+9+9-3=24
3,9,9,10 --- (9+9-10)×3=24
3,9,10,10 --- (9-10÷10)×3=24
4,4,4,4 --- 4+4+4×4=24
4,4,4,5 --- (4÷4+5)×4=24
4,4,4,6 --- 4+4×6-4=24
4,4,4,7 --- (4+4)×(7-4)=24
4,4,4,8 --- 4×(4+8÷4)=24
4,4,4,9 --- 4+4×(9-4)=24
4,4,4,10 --- (4×4-10)×4=24
4,4,5,5 --- 4×(5+5-4)=24
4,4,5,6 --- (5-4)×6×4=24
4,4,5,7 --- (4-5+7)×4=24
4,4,5,8 --- 4+5×(8-4)=24
4,4,5,10 --- 4-(5-10)×4=24
4,4,6,8 --- (4-6+8)×4=24
4,4,6,9 --- 4÷6×9×4=24
4,4,6,10 --- 4+6+10+4=24
4,4,7,7 --- 7×(4-4÷7)=24
4,4,7,8 --- 4×7-8+4=24
4,4,7,9 --- 4+7+9+4=24
4,4,7,10 --- (10-7)×(4+4)=24
4,4,8,8 --- 4+8+8+4=24
4,4,8,9 --- 4×9-8-4=24
4,4,8,10 --- 4+8×10÷4=24
4,4,10,10 --- (10×10-4)÷4=24
4,5,5,5 --- (5+5÷5)×4=24
4,5,5,6 --- 5-5+6×4=24
4,5,5,7 --- (7-5÷5)×4=24
4,5,5,8 --- 8×(4-5÷5)=24
4,5,5,9 --- 5×(9-5)+4=24
4,5,5,10 --- 5+5+10+4=24
4,5,6,6 --- (5+6÷6)×4=24
4,5,6,7 --- (5-6+7)×4=24
4,5,6,8 --- 8×(5-6+4)=24
4,5,6,9 --- 5+6+9+4=24
4,5,6,10 --- 5×6-10+4=24
4,5,7,7 --- (5+7÷7)×4=24
4,5,7,8 --- 5+7+8+4=24
4,5,7,9 --- 7×(9-5)-4=24
4,5,7,10 --- (7-5)×10+4=24
4,5,8,8 --- (5+8÷8)×4=24
4,5,8,9 --- (5-8+9)×4=24
4,5,8,10 --- 5×(8÷10+4)=24
4,5,9,9 --- (5+9÷9)×4=24
4,5,9,10 --- (5-9+10)×4=24
4,5,10,10 --- (5+10÷10)×4=24
4,6,6,6 --- (6+6-6)×4=24
4,6,6,7 --- 6+6×(7-4)=24
4,6,6,8 --- 6+6+8+4=24
4,6,6,9 --- 6+9×(6-4)=24
4,6,6,10 --- 6×(6+10)÷4=24
4,6,7,7 --- 6+7+7+4=24
4,6,7,8 --- (8-7)×6×4=24
4,6,7,9 --- 6×(7+9)÷4=24
4,6,7,10 --- 7×(10-6)-4=24
4,6,8,8 --- (6+8-8)×4=24
4,6,8,9 --- 6+8×9÷4=24
4,6,8,10 --- 8-(6-10)×4=24
4,6,9,9 --- (6+9-9)×4=24
4,6,9,10 --- (6+9×10)÷4=24
4,6,10,10 --- (6+10-10)×4=24
4,7,7,7 --- (7-7÷7)×4=24
4,7,7,8 --- (7+7-8)×4=24
4,7,8,8 --- (7-8÷8)×4=24
4,7,8,9 --- (7+8-9)×4=24
4,7,8,10 --- 10+8×7÷4=24
4,7,9,9 --- (7-9÷9)×4=24
4,7,9,10 --- (7+9-10)×4=24
4,7,10,10 --- (7-10÷10)×4=24
4,8,8,8 --- 8+8×8÷4=24
4,8,8,9 --- 8×(8-9+4)=24
4,8,8,10 --- (8+8-10)×4=24
4,8,9,9 --- (4-9÷9)×8=24
4,8,9,10 --- 8×(9-10+4)=24
4,8,10,10 --- 8+10+10-4=24
4,9,9,10 --- 9+9+10-4=24
5,5,5,5 --- 5×5-5÷5=24
5,5,5,6 --- 5×5-6+5=24
5,5,5,9 --- 5+5+9+5=24
5,5,6,6 --- 5×(6-6÷5)=24
5,5,6,7 --- 6-7+5×5=24
5,5,6,8 --- 5+6+8+5=24
5,5,7,7 --- 5+7+7+5=24
5,5,7,8 --- 7-8+5×5=24
5,5,7,10 --- (5+7)×10÷5=24
5,5,8,8 --- 5×5-8÷8=24
5,5,8,9 --- 8-9+5×5=24
5,5,8,10 --- 8×(5+10)÷5=24
5,5,9,9 --- 5×5-9÷9=24
5,5,9,10 --- 9-10+5×5=24
5,5,10,10 --- 5×5-10÷10=24
5,6,6,6 --- 6×(5-6÷6)=24
5,6,6,7 --- 6+6+7+5=24
5,6,6,8 --- 6+6×(8-5)=24
5,6,6,9 --- 6×9-6×5=24
5,6,6,10 --- (6+6)×10÷5=24
5,6,7,7 --- (5-7÷7)×6=24
5,6,7,8 --- 6×(7-8+5)=24
5,6,7,9 --- 6+9×(7-5)=24
5,6,8,8 --- 8×(6-8+5)=24
5,6,8,9 --- 6×(8-9+5)=24
5,6,8,10 --- 6×8÷10×5=24
5,6,9,9 --- 9-(6-9)×5=24
5,6,9,10 --- 6+9×10÷5=24
5,6,10,10 --- 6×(10+10)÷5=24
5,7,7,9 --- (9-7)×(7+5)=24
5,7,7,10 --- 10+7×(7-5)=24
5,7,8,8 --- (7+8)×8÷5=24
5,7,8,9 --- 8×(7-9+5)=24
5,7,8,10 --- (10-8)×(7+5)=24
5,7,9,10 --- 9-(7-10)×5=24
5,7,10,10 --- 10+7×10÷5=24
5,8,8,8 --- 8×8-8×5=24
5,8,8,9 --- 8×9÷(8-5)=24
5,8,8,10 --- 8+8×10÷5=24
5,9,10,10 --- 9+10+10-5=24
6,6,6,6 --- 6+6+6+6=24
6,6,6,8 --- (6+6-8)×6=24
6,6,6,9 --- 6+6×(9-6)=24
6,6,6,10 --- 6×10-6×6=24
6,6,7,9 --- (6+7-9)×6=24
6,6,7,10 --- 6-(7-10)×6=24
6,6,8,8 --- 6×8÷(8-6)=24
6,6,8,9 --- (8-6)×9+6=24
6,6,8,10 --- (6+8-10)×6=24
6,6,9,10 --- (9-6)×10-6=24
6,7,7,10 --- (7+7-10)×6=24
6,7,8,9 --- 8÷(9-7)×6=24
6,7,8,10 --- 8×(7-10+6)=24
6,7,9,9 --- (7+9)×9÷6=24
6,7,10,10 --- (10-7)×10-6=24
6,8,8,8 --- 8+8×(8-6)=24
6,8,8,9 --- (8+8)×9÷6=24
6,8,8,10 --- 8×(8+10)÷6=24
6,8,9,9 --- 8×(9+9)÷6=24
6,8,9,10 --- 9×(10-8)+6=24
6,9,9,10 --- 9+9×10÷6=24
6,10,10,10 --- 10+10+10-6=24
7,7,9,10 --- 10+(9-7)×7=24
7,8,8,9 --- 8+8×(9-7)=24
7,8,8,10 --- 8×10-8×7=24
7,8,9,10 --- 8×9÷(10-7)=24
7,8,10,10 --- 10-(8-10)×7=24
8,8,8,10 --- 8+8×(10-8)=24