算24点的技巧与经典题目.doc

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算24点的技巧　　“巧算24点”是一种数学游戏，游戏方式简单易学，能健脑益智，是一项极为有益的活动．　　“巧算24点”的游戏内容如下：一副牌中抽去大小王剩下52张，（如果初练也可只用1～10这40张牌）任意抽取4张牌（称牌组），用加、减、乘、除（可加括号）把牌面上的数算成24．每张牌必须用一次且只能用一次，如抽出的牌是3、8、8、9，那么算式为（9—8）×8×3或3×8＋（9—8）或（9—8÷8）×3等．　　“算24点”作为一种扑克牌智力游戏，还应注意计算中的技巧问题．计算时，我们不可能把牌面上的4个数的不同组合形式——去试，更不能瞎碰乱凑．这里向大家介绍几种常用的、便于学习掌握的方法：　　1．利用3×8＝24、4×6＝24求解．　　把牌面上的四个数想办法凑成3和8、4和6，再相乘求解．如3、3、6、10可组成（10—6÷3）×3＝24等．又如2、3、3、7可组成（7＋3—2）×3＝24等．实践证明，这种方法是利用率最大、命中率最高的一种方法．　　2．利用0、11的运算特性求解．　　如3、4、4、8可组成3×8＋4—4＝24等．又如4、5、J、K可组成11×（5—4）＋13＝24等．　　3．在有解的牌组中，用得最为广泛的是以下六种解法：（我们用a、b、c、d表示牌面上的四个数）　　①(a—b）×（c＋d）　　如（10—4）×（2＋2）＝24等．　　②（a＋b）÷c×d 　　如（10＋2）÷2×4＝24等．　　③（a－b÷c）×d 　　如（3—2÷2）×12＝24等．　　④（a＋b－c）×d 　　如（9＋5—2）×2＝24等．　　⑤a×b＋c—d 　　如11×3＋l—10＝24等．　　⑥（a－b）×c＋d 　　如（4—l）×6＋6＝24等．　　游戏时，同学们不妨按照上述方法试一试．　　需要说明的是：经计算机准确计算，一副牌（52张）中，任意抽取4张可有1820种不同组合，其中有458个牌组算不出24点，如A、A、A、5．不难看出，“巧算24点”能极大限度地调动眼、脑、手、口、耳多种感官的协调活动，对于培养我们快捷的心算能力和反应能力很有帮助．算24点经典题目算24点经典题目 5 5 5 1：5（5-1/5）=24 2 7 9 10: ((7-(2-9))+10)=24 2 7 10 10: ((2×(7+10))-10)=24 2 8 8 8: ((2×(8+8))-8)=24 2 8 8 9: ((2-(8-9))×8)=24 2 8 8 10: ((8-(2-8))+10)=24 2 8 9 9: ((2+(9/9))×8)=24 2 8 9 10: ((2×(8+9))-10)=24 2 8 10 10: ((2+(10/10))×8)=24 2 9 10 10: ((9+(10/2))+10)=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)+(3×5))=24 3 3 3 6: ((3×(3+3))+6)=24 3 3 3 7: ((7+(3/3))×3)=24 3 3 3 8: ((3+(3-3))×8)=24 3 3 3 9: ((9-(3/3))×3)=24 3 3 3 10: ((3×(10-3))+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-(3-4))×6)=24 3 3 4 7: ((4-(3-7))×3)=24 3 3 4 8: ((3×(4-3))×8)=24 3 3 4 9: ((3+(3×4))+9)=24 3 3 5 5: ((5×5)-(3/3))=24 3 3 5 6: ((3+(3×5))+6)=24 3 3 5 7: (((3×5)-7)×3)=24 3 3 5 9: ((5+(9/3))×3)=24 3 3 5 10: ((3-(3/5))×10)=24 3 3 6 6: ((6+(6/3))×3)=24 3 3 6 7: ((3×(3+7))-6)=24 3 3 6 8: ((8×(3+6))/3)=24 3 3 6 9: ((3+(3×9))-6)=24 3 3 6 10: ((10-(3+3))×6)=24 3 3 7 7: ((3+(3/7))×7)=24 3 3 7 8: ((7+(3×3))+8)=24 3 3 7 9: ((7/(3/9))+3)=24 3 3 8 8: (8/(3-(8/3)))=24 3 3 8 9: ((3×(3+8))-9)=24 3 3 8 10: ((3+(3+8))+10)=24 3 3 9 9: ((3+(3+9))+9)=24 3 3 9 10: ((3+(3×10))-9)=24 3 4 4 4: ((4×(3+4))-4)=24 3 4 4 5: ((3+(4×4))+5)=24 3 4 4 6: ((3+(4/4))×6)=24 3 4 4 7: ((3-(4-7))×4)=24 3 4 4 8: ((3+(4-4))×8)=24 3 4 4 9: ((4-(4/3))×9)=24 3 4 4 10: ((4×(10-3))-4)=24 3 4 5 5: ((3+(5×5))-4)=24 3 4 5 6: ((3-(4-5))×6)=24 3 4 5 7: ((3×(7-5))×4)=24 3 4 5 8: ((3×(5-4))×8)=24 3 4 5 9: ((4-(5-9))×3)=24 3 4 5 10: ((3×(4/5))×10)=24 3 4 6 6: ((3×(4+6))-6)=24 3 4 6 8: ((3×(8-6))×4)=24 3 4 6 9: ((3-(6-9))×4)=24 3 4 6 10: ((3×(10-4))+6)=24 3 4 7 7: ((3+(4×7))-7)=24 3 4 7 8: ((4×(7-3))+8)=24 3 4 7 9: ((3×(4+7))-9)=24 3 4 7 10: ((3+(4+7))+10)=24 3 4 8 9: ((3+(4+8))+9)=24 3 4 8 10: ((3×(10-8))×4)=24 3 4 9 9: ((3×(9-4))+9)=24 3 4 10 10: ((4+(3×10))-10)=24 3 5 5 6: ((3×(5+5))-6)=24 3 5 5 7: ((7+(5/5))×3)=24 3 5 5 8: ((3+(5-5))×8)=24 3 5 5 9: ((3+(9/5))×5)=24 3 5 6 6: ((3-(5-6))×6)=24 3 5 6 7: ((6×(5+7))/3)=24 3 5 6 8: ((3×(6-5))×8)=24 3 5 6 9: ((3×(5+6))-9)=24 3 5 6 10: ((3+(5+6))+10)=24 3 5 7 8: ((7×(8-5))+3)=24 3 5 7 9: ((3+(5+7))+9)=24 3 5 7 10: ((5-(7-10))×3)=24 3 5 8 8: ((3+(5+8))+8)=24 3 5 8 9: ((5+(3×9))-8)=24 3 5 9 9: ((5/(3/9))+9)=24 3 5 9 10: ((3×(10-5))+9)=24 3 5 10 10: ((10-(10/5))×3)=24 3 6 6 6: ((3+(6/6))×6)=24 3 6 6 7: ((3-(6-7))×6)=24 3 6 6 8: ((3+(6-6))×8)=24 3 6 6 9: ((3+(6+6))+9)=24 3 6 6 10: ((10×(6-3))-6)=24 3 6 7 7: ((3+(7/7))×6)=24 3 6 7 8: ((3+(6+7))+8)=24 3 6 7 9: ((6-(7-9))×3)=24 3 6 7 10: ((6/(3/7))+10)=24 3 6 8 8: ((3+(8/8))×6)=24 3 6 8 9: ((3-(8-9))×6)=24 3 6 8 10: ((6-(8-10))×3)=24 3 6 9 9: ((3+(9/9))×6)=24 3 6 9 10: ((3-(9-10))×6)=24 3 6 10 10: ((3-(6/10))×10)=24 3 7 7 7: ((3+(7+7))+7)=24 3 7 7 8: ((3+(7-7))×8)=24 3 7 7 9: ((9-(7/7))×3)=24 3 7 7 10: ((7×(10-7))+3)=24 3 7 8 8: ((3×(8-7))×8)=24 3 7 8 9: ((7-(8-9))×3)=24 3 7 9 9: ((7+(9/9))×3)=24 3 7 9 10: ((7+(3×9))-10)=24 3 7 10 10: ((7-(3-10))+10)=24 3 8 8 8: ((3+(8-8))×8)=24 3 8 8 9: ((3×(9-8))×8)=24 3 8 8 10: (((8×10)-8)/3)=24 3 8 9 9: ((3×(8×9))/9)=24 3 8 9 10: ((3×(10-9))×8)=24 3 8 10 10: ((3×(8×10))/10)=24 3 9 9 9: ((9-(3-9))+9)=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: ((5+(4/4))×4)=24 4 4 4 6: ((4+(4-4))×6)=24 4 4 4 7: ((7-(4/4))×4)=24 4 4 4 8: ((4×(4+4))-8)=24 4 4 4 9: ((4×(9-4))+4)=24 4 4 4 10: (((4×4)-10)×4)=24 4 4 5 5: ((4+(4/5))×5)=24 4 4 5 6: ((4×(5-4))×6)=24 4 4 5 7: ((4-(5-7))×4)=24 4 4 5 8: ((4+(4-5))×8)=24 4 4 5 10: ((4×(10-5))+4)=24 4 4 6 8: ((4-(6-8))×4)=24 4 4 6 9: ((4×(4/6))×9)=24 4 4 6 10: ((4+(4+6))+10)=24 4 4 7 7: ((4-(4/7))×7)=24 4 4 7 8: ((4+(4×7))-8)=24 4 4 7 9: ((4+(4+7))+9)=24 4 4 7 10: ((4+4)×(10-7))=24 4 4 8 8: ((4+(4+8))+8)=24 4 4 8 9: (((4×9)-4)-8)=24 4 4 8 10: ((4-(8-10))×4)=24 4 4 10 10: (((10×10)-4)/4)=24 4 5 5 5: ((4+(5×5))-5)=24 4 5 5 6: ((4+(5-5))×6)=24 4 5 5 7: ((7-(5/5))×4)=24 4 5 5 8: ((4-(5/5))×8)=24 4 5 5 9: ((5×(9-5))+4)=24 4 5 5 10: ((4+(5+5))+10)=24 4 5 6 6: ((4×(6-5))×6)=24 4 5 6 7: ((5-(6-7))×4)=24 4 5 6 8: ((4+(5-6))×8)=24 4 5 6 9: ((4+(5+6))+9)=24 4 5 6 10: ((4+(5×6))-10)=24 4 5 7 7: ((5+(7/7))×4)=24 4 5 7 8: ((4+(5+7))+8)=24 4 5 7 9: ((5+(4×7))-9)=24 4 5 7 10: ((10×(7-5))+4)=24 4 5 8 8: ((5-(8/4))×8)=24 4 5 8 9: ((4×(9-5))+8)=24 4 5 8 10: ((4-(8/5))×10)=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: ((4+(6-6))×6)=24 4 6 6 7: ((4×(7-6))×6)=24 4 6 6 8: ((4+(6+6))+8)=24 4 6 6 9: ((6×(9-4))-6)=24 4 6 6 10: ((6×(6+10))/4)=24 4 6 7 7: ((4+(6+7))+7)=24 4 6 7 8: ((4+(6-7))×8)=24 4 6 7 9: ((6×(7+9))/4)=24 4 6 7 10: ((6+(4×7))-10)=24 4 6 8 8: ((4×(6×8))/8)=24 4 6 8 9: ((4-(8/6))×9)=24 4 6 8 10: ((4×(10-6))+8)=24 4 6 9 9: ((4×(6×9))/9)=24 4 6 9 10: ((4×(10-9))×6)=24 4 6 10 10: ((4×(6×10))/10)=24 4 7 7 7: ((7-(7/7))×4)=24 4 7 7 8: ((4-(7/7))×8)=24 4 7 8 8: ((4+(7-8))×8)=24 4 7 8 9: ((7+(8-9))×4)=24 4 7 8 10: ((7/(4/8))+10)=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: ((4-(8/8))×8)=24 4 8 8 9: ((4+(8-9))×8)=24 4 8 8 10: ((8+(8-10))×4)=24 4 8 9 9: ((4-(9/9))×8)=24 4 8 9 10: ((4+(9-10))×8)=24 4 8 10 10: ((4-(10/10))×8)=24 4 9 9 10: ((9-(4-9))+10)=24 5 5 5 5: ((5×5)-(5/5))=24 5 5 5 6: ((5+(5×5))-6)=24 5 5 5 9: ((5+(5+5))+9)=24 5 5 6 6: ((5+(5-6))×6)=24 5 5 6 7: ((6+(5×5))-7)=24 5 5 6 8: ((5+(5+6))+8)=24 5 5 7 7: ((5+(5+7))+7)=24 5 5 7 8: ((5+(5-7))×8)=24 5 5 7 10: ((10×(5+7))/5)=24 5 5 8 8: ((5×5)-(8/8))=24 5 5 8 9: ((5×(8-5))+9)=24 5 5 8 10: ((5-(10/5))×8)=24 5 5 9 9: ((5×5)-(9/9))=24 5 5 9 10: ((9+(5×5))-10)=24 5 5 10 10: ((5×5)-(10/10))=24 5 6 6 6: ((5-(6/6))×6)=24 5 6 6 7: ((5+(6+6))+7)=24 5 6 6 8: ((6×(8-5))+6)=24 5 6 6 9: ((6×9)-(5×6))=24 5 6 6 10: ((6×(10-5))-6)=24 5 6 7 7: ((5-(7/7))×6)=24 5 6 7 8: ((5+(7-8))×6)=24 5 6 7 9: ((9×(7-5))+6)=24 5 6 8 8: ((5+(6-8))×8)=24 5 6 8 9: ((5+(8-9))×6)=24 5 6 8 10: ((5×(6×8))/10)=24 5 6 9 9: ((5×(9-6))+9)=24 5 6 9 10: ((5+(9-10))×6)=24 5 6 10 10: ((5-(10/10))×6)=24 5 7 7 9: ((5+7)×(9-7))=24 5 7 7 10: ((7×(7-5))+10)=24 5 7 8 8: ((8×(7-5))+8)=24 5 7 8 9: ((5+(7-9))×8)=24 5 7 8 10: ((5+7)×(10-8))=24 5 7 9 10: ((5×(10-7))+9)=24 5 7 10 10: ((7/(5/10))+10)=24 5 8 8 8: (((5×8)-8)-8)=24 5 8 8 9: ((8/(8-5))×9)=24 5 8 8 10: ((5+(8-10))×8)=24 5 9 10 10: ((9-(5-10))+10)=24 6 6 6 6: ((6+(6+6))+6)=24 6 6 6 8: ((6+(6-8))×6)=24 6 6 6 9: ((6×(6×6))/9)=24 6 6 6 10: ((6×10)-(6×6))=24 6 6 7 9: ((6+(7-9))×6)=24 6 6 7 10: ((6×(10-7))+6)=24 6 6 8 8: ((6/(8-6))×8)=24 6 6 8 9: ((6+(6-9))×8)=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: ((6/(9-7))×8)=24 6 7 8 10: ((6+(7-10))×8)=24 6 7 9 9: ((9×(7+9))/6)=24 6 7 10 10: ((10×(10-7))-6)=24 6 8 8 8: ((8×(8-6))+8)=24 6 8 8 9: ((9×(8+8))/6)=24 6 8 8 10: ((6/(10-8))×8)=24 6 8 9 9: ((8/(9-6))×9)=24 6 8 9 10: ((9×(10-8))+6)=24 6 9 9 10: ((9/(6/10))+9)=24 6 10 10 10: ((10-(6-10))+10)=24 7 7 9 10: ((7×(9-7))+10)=24 7 8 8 9: ((8×(9-7))+8)=24 7 8 8 10: ((8×10)-(7×8))=24 7 8 9 10: ((8/(10-7))×9)=24 7 8 10 10: ((7×(10-8))+10)=24 8 8 8 10: ((8×(10-8))+8)=24

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