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1.75亿学生的选择
用1，9，12，13怎样能得24？
13-9-1后面乘12
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12加12等于24
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1.75亿学生的选择
4 9 9 1四个数字怎么算等于24
恰恰帅气171
同意1楼的答案.
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其他类似问题
扫描下载二维码24点3个9一个13怎么算
24点3个9一个13怎么算
09-10-18 &匿名提问
[(-5)X(-13)+7]÷3
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1.4.9.9无解 1.1.5.9无解通过计算机利用穷举法知道是无解的24点游戏的算法与源程序高一7 高雅 Jan 5th. 2002任务说明24点游戏是一个大众化的益智游戏.任意给四张扑克牌(不包括大小王),只能够用加,减,乘,除以及适当的括号连接这四张牌,无论顺序,使计算结果为24,或者宣布根本就是无解的.需要注意的是,每张牌必须运算,并且只能运算一次,J,Q,K可设置为11,12,13.本程序目的就是算出一组牌的所有解(不同形式的式子算不同解),如没有则输出无解.算法说明首先解决图形扑克牌的显示问题.我选择了Qcard.dll.运用其中的DrawCard过程可轻松实现扑克的显示问题,在源程序中会有具体用法.接下来是24点算法的讨论.首先想到的是用穷举表达式的方法,然后求值.然而,由于括号的存在,使穷举表达式并非易事.实际上,括号的作用仅仅是提高运算的优先级而已,如果我们规定符号的优先级,一样可以达到要求.具体来说,设四张牌为a,b,c,d,运算符为①,②,③,表达式为a ① b ② c ③ .如果强制规定①,②,③的优先顺序,就不必考虑括号问题了.而这3个运算符的运算顺序有3!=6种,分别是:1.①②③ 2.①③② 3.②①③ 4.②③① 5.③①② 6.③②①等价的表达式分别是:1.((a①b②)c③) 2.(a①b)②(c③d) 3.(a①(b②c))③d4.a①((b②c)③d) 5.(a①b)②(c③d) 6. a①(b②(c③d))显然,2和5是相同的,因此只考虑5种情况.这样,括号的问题就解决了.接下来,就是生成a,b,c,d的全排列,注意去掉其中的相同排列.去除的方法很多,比如字典排序等,我用的是另一种方法.用循环的嵌套生成a,b,c,d的24种全排列,记录在数组中.把每一组数当作一个四位的14进制数,把这24个数全部转化为十进制(如(*143+5*142+2*14+9).这样,如果两个排列完全相同,则得到的十进制数是相等的.这样,通过对这些十进制的比较,就可以比较这些排列的相同情况.一旦遇到相同的排列,就标记上.最后生成一组没有重复的排列.对这组排列进行以上方法的运算,就可以得到所有的结果了.注意在运算过程中除法的特殊性——除数不能为零.因为可能会用到除法,所以要考虑精度问题,这里通过结果减去24取绝对值与一个接近0的小数比较,如小于它,即可判定结果是24.附:其他待决的问题:图形扑克牌的遮挡问题.当窗口中的扑克牌被遮挡后,扑克牌不会重新画上,造成扑克牌遮挡后显示不全问题.应寻找Qcard.dll的有关参数.形式不同而实质相同的解的问题.有些解虽然形式不同,但其实质是完全相同的.如3*((11+4)-7)和3*(11+(4-7)),实际上只是一种解.去掉这些相同解的问题情况较多,其较为繁琐,有待解决.多余括号好问题.有些解的括号是多余的,应在输出前去掉.改进程序的可玩性.增加玩家输入表达式的功能,并判断对错,还可以加上时间限制,使玩家参与到游戏中.程序框图VB源程序代码'需要声明所有用到的变量Option Explicit'声明全局变量,数组Dim cards(1 To 4) As Single, card(1 To 4) As SingleDim result(1 To 24, 0 To 4) As Integer, final(1 To 24, 1 To 4) As Integer, temp(1 To 24) As LongDim nokey As Boolean, total As Integer, n1 As Integer, n2 As Integer, n3 As Integer, n4 As Integer, a As Integer, b As Integer, c As Integer, d As Integer, op1 As Integer, op2 As Integer, op3 As Integer, answer1 As Single, answer2 As Single, answer3 As Single, color As IntegerDim i As Integer, j As Integer, t As Integer'声明zero常量,设置0的标准,处理除法的精度问题Const zero = 0.00001'初始化QCARD32.DLLPrivate Declare Function InitializeDeck Lib &qcard32.dll& (ByVal hwin As Long) As Integer'DrawCard 子程序,画出扑克牌图样在FORM窗体及 窗体上的图片框'用法:'hwnd ---- 需要画图的对象句柄'nCard --- 扑克牌编号 其编号如下'1-13 梅花 14-26 方块 27-39 红心 40-52 黑桃 小王-110 大王-111'x,y 位置Private Declare Sub DrawCard Lib &qcard32.dll& (ByVal hwnd As Long, ByVal nCard As Integer, ByVal x As Integer, ByVal y As Integer)'DrawBack 子程序,画出扑克牌的背面图案,共六种 按 1--6 编号Private Declare Sub DrawBack Lib &qcard32.dll& (ByVal hwnd As Long, ByVal nCard As Long, ByVal x As Long, ByVal y As Long)'GetCardSuit 函数,求 nCard 的点数 1-13'Private Declare Function GetCardSuit Lib &qcard32.dll& (ByVal nCard As Long) As Long'GetCardValue 函数,求 nCard 的花色 0:鬼牌 1:梅花 2:方块 3:红心 4:黑桃'Private Declare Function GetCardValue Lib &qcard32.dll& (ByVal nCard As Long) As Long'Form_Load过程,初始化Private Sub Form_Load()Randomize TimerCall InitializeDeck(Me.hwnd)Command3.Enabled = FalseEnd Sub'answer函数,返回x与y做operator运算后的值,-100为错误标志Private Function answer(x As Single, y As Single, operator As Integer) As SingleSelect Case operatorCase 1answer = x + yExit FunctionCase 2answer = x - yExit FunctionCase 3answer = x * yExit FunctionCase 4If y = 0 Thenanswer = -100Exit FunctionElseanswer = x / yExit FunctionEnd IfEnd Selectanswer = -100End Function'operate函数,返回数值op所对应的四则运算符号Private Function operate(op As Integer) As StringSelect Case opCase 1operate = &+&Case 2operate = &-&Case 3operate = &*&Case 4operate = &/&End SelectEnd Function'search过程,去掉数组result中相同的元素,存入数组final中Private Sub search()For i = 1 To 24result(i, 0) = 0temp(i) = result(i, 1) * 14 ^ 3 + result(i, 2) * 14 ^ 2 + result(i, 3) * 14 + result(i, 4)Next iFor i = 1 To 23For j = i + 1 To 24If temp(i) = temp(j) Then result(i, 0) = 1Next jNext iFor i = 1 To 24If result(i, 0) = 1 Then GoTo 1t = t + 1For j = 1 To 4final(t, j) = result(i, j)Next j1 Next iEnd Sub'Main过程,用于计算四个数通过不同运算得到24的所有情况,并输出结果Private Sub Main()For op1 = 1 To 4For op2 = 1 To 4For op3 = 1 To 4'1·形如( a @ b ) @ c ) @ d 的表达式answer1 = answer(cards(1), cards(2), op1)answer2 = answer(answer1, cards(3), op2)answer3 = answer(answer2, cards(4), op3)If answer1 -100 And answer2 -100 And answer3 -100 ThenIf Abs(answer3 - 24) & zero Thennokey = Falsetotal = total + 1Text1.Text = Text1.Text + &((& + Trim$(Str$(cards(1))) + operate(op1) + Trim$(Str$(cards(2))) + &)& + operate(op2) + Trim$(Str$(cards(3))) + &)& + operate(op3) + Trim$(Str$(cards(4))) + & &'若本行已有三个式子,就换行If total Mod 3 = 0 ThenText1.Text = Text1.Text + Chr$(13) + Chr$(10)End IfEnd IfEnd If'2·形如( a @ b ) @ (c @ d) 的表达式answer1 = answer(cards(1), cards(2), op1)answer2 = answer(cards(3), cards(4), op3)answer3 = answer(answer1, answer2, op2)If answer1 -100 And answer2 -100 And answer3 -100 ThenIf Abs(answer3 - 24) & zero Thennokey = Falsetotal = total + 1Text1.Text = Text1.Text + &(& + Trim$(Str$(cards(1))) + operate(op1) + Trim$(Str$(cards(2))) + &)& + operate(op2) + &(& + Trim$(Str$(cards(3))) + operate(op3) + Trim$(Str$(cards(4))) + &)& + & &'若本行已有三个式子,就换行If total Mod 3 = 0 ThenText1.Text = Text1.Text + Chr$(13) + Chr$(10)End IfEnd IfEnd If'3·形如( a @ ( b @ c ) ) @ d 的表达式answer1 = answer(cards(2), cards(3), op2)answer2 = answer(cards(1), answer1, op1)answer3 = answer(answer2, cards(4), op3)If answer1 -100 And answer2 -100 And answer3 -100 ThenIf Abs(answer3 - 24) & zero Thennokey = Falsetotal = total + 1Text1.Text = Text1.Text + &(& + Trim$(Str$(cards(1))) + operate(op1) + &(& + Trim$(Str$(cards(2))) + operate(op2) + Trim$(Str$(cards(3))) + &))& + operate(op3) + Trim$(Str$(cards(4))) + & &'若本行已有三个式子,就换行If total Mod 3 = 0 ThenText1.Text = Text1.Text + Chr$(13) + Chr$(10)End IfEnd IfEnd If'4·形如 a @ ( ( b @ c ) @ d ) 的表达式answer1 = answer(cards(2), cards(3), op2)answer2 = answer(answer1, cards(4), op3)answer3 = answer(cards(1), answer2, op1)If answer1 -100 And answer2 -100 And answer3 -100 ThenIf Abs(answer3 - 24) & zero Thennokey = Falsetotal = total + 1Text1.Text = Text1.Text + Trim$(Str$(cards(1))) + operate(op1) + &((& + Trim$(Str$(cards(2))) + operate(op2) + Trim$(Str$(cards(3))) + &)& + operate(op3) + Trim$(Str$(cards(4))) + &)& + & &'若本行已有三个式子,就换行If total Mod 3 = 0 ThenText1.Text = Text1.Text + Chr$(13) + Chr$(10)End IfEnd IfEnd If'5·形如 a @ ( b @ ( c @ d ) ) 的表达式answer1 = answer(cards(3), cards(4), op3)answer2 = answer(cards(2), answer1, op2)answer3 = answer(cards(1), answer2, op1)If answer1 -100 And answer2 -100 And answer3 -100 ThenIf Abs(answer3 - 24) & zero Thennokey = Falsetotal = total + 1Text1.Text = Text1.Text + Trim$(Str$(cards(1))) + operate(op1) + &(& + Trim$(Str$(cards(2))) + operate(op2) + &(& + Trim$(Str$(cards(3))) + operate(op3) + Trim$(Str$(cards(4))) + &))& + & &'若本行已有三个式子,就换行If total Mod 3 = 0 ThenText1.Text = Text1.Text + Chr$(13) + Chr$(10)End IfEnd IfEnd IfNext op3Next op2Next op1End Sub'Card1_MouseDown过程,按左键点击纸牌加1,按右键减1Private Sub Card1_MouseDown(Button As Integer, Shift As Integer, x As Single, y As Single)Select Case Button'按左键Case 1If card(4) = 13 Thencard(4) = 1Elsecard(4) = card(4) + 1End If'按右键Case 2If card(4) = 1 Thencard(4) = 13Elsecard(4) = card(4) - 1End IfEnd Select'随机产生变化后的花色color = Int(Rnd() * 4)'重画纸牌Call DrawCard(Me.hwnd, color * 13 + card(4), 10, 10)End Sub'Card2_MouseDown过程,按左键点击纸牌加1,按右键减1Private Sub Card2_MouseDown(Button As Integer, Shift As Integer, x As Single, y As Single)Select Case Button'按左键Case 1If card(3) = 13 Thencard(3) = 1Elsecard(3) = card(3) + 1End If'按右键Case 2If card(3) = 1 Thencard(3) = 13Elsecard(3) = card(3) - 1End IfEnd Select'随机产生变化后的花色color = Int(Rnd() * 4)'重画纸牌Call DrawCard(Me.hwnd, color * 13 + card(3), 10 + 85, 10)End Sub'Card3_MouseDown过程,按左键点击纸牌加1,按右键减1Private Sub Card3_MouseDown(Button As Integer, Shift As Integer, x As Single, y As Single)Select Case Button'按左键Case 1If card(2) = 13 Thencard(2) = 1Elsecard(2) = card(2) + 1End If'按右键Case 2If card(2) = 1 Thencard(2) = 13Elsecard(2) = card(2) - 1End IfEnd Select'随机产生变化后的花色color = Int(Rnd() * 4)'重画纸牌Call DrawCard(Me.hwnd, color * 13 + card(2), 10 + 2 * 85, 10)End Sub'Card4_MouseDown过程,按左键点击纸牌加1,按右键减1Private Sub Card4_MouseDown(Button As Integer, Shift As Integer, x As Single, y As Single)Select Case Button'按左键Case 1If card(1) = 13 Thencard(1) = 1Elsecard(1) = card(1) + 1End If'按右键Case 2If card(1) = 1 Thencard(1) = 13Elsecard(1) = card(1) - 1End IfEnd Select'随机产生变化后的花色color = Int(Rnd() * 4)'重画纸牌Call DrawCard(Me.hwnd, color * 13 + card(1), 10 + 3 * 85, 10)End Sub'Command1_Click过程,点击洗牌按钮画出纸牌背面Private Sub Command1_Click()'随机产生纸牌背面的样式color = Int(Rnd() * 6 + 1)'画出纸牌背面Call DrawBack(Me.hwnd, color, 10, 10)Call DrawBack(Me.hwnd, color, 95, 10)Call DrawBack(Me.hwnd, color, 180, 10)Call DrawBack(Me.hwnd, color, 265, 10)'禁用答案按钮Command3.Enabled = FalseEnd Sub'Command2_Click过程,点击发牌按钮画出随机产生的纸牌Private Sub Command2_Click()'清空答案Text1.Text = &&'随机产生的纸牌,并画出For i = 1 To 4card(i) = Int(Rnd() * 13 + 1)color = Int(Rnd() * 4)Call DrawCard(Me.hwnd, color * 13 + card(i), 10 + (4 - i) * 85, 10)Next i'开启答案按钮Command3.Enabled = TrueEnd Sub'Command3_Click过程,点击答案按钮计算结果Private Sub Command3_Click()'清空解的数量Label1.Caption = &&'默认设置为无解nokey = True'解的计数器清零total = 0'临时变量清零i = 0j = 0t = 0'产生24种全排列For n1 = 1 To 4For n2 = 1 To 4If n2 = n1 Then GoTo 2For n3 = 1 To 4If n3 = n1 Or n3 = n2 Then GoTo 3n4 = 10 - n1 - n2 - n3i = i + 1result(i, 1) = card(n1)result(i, 2) = card(n2)result(i, 3) = card(n3)result(i, 4) = card(n4)3 Next n32 Next n2Next n1'调用search过程,去掉重复排列Call search'调用Main过程,寻找答案For i = 1 To tFor j = 1 To 4cards(j) = final(i, j)Next jCall MainNext i'输出解的情况If nokey = False Then Label1.Caption = &共有& + Trim$(Str$(total)) + &组解!& Else Label1.Caption = &无解!&'禁止答案按钮Command3.Enabled = FalseEnd Sub五,程序界面NY比较temp(i)与temp(j)是否相等For j=i+1 to 24For i=1 to 23初始化变量,数组For i=1 to 24初始化重复排列的标志result(1..24,0)=0排列存入数组result(1..24,1..4)全排列循环终止3重循环产生24种全排列随机产生四张扑克牌将全排列所对应的十进制数存入temp(1..24)Next i设置重复排列的标志result(i,0)=1计数器t=t+1Next jNext i结束输出解的个数或无解结束循环final中的排列计算形如 a @ ( b @ ( c @ d ) ) 的表达式如等于24则输出计算形如 a @ ( ( b @ c ) @ d ) 的表达式如等于24则输出计算形如( a @ ( b @ c ) ) @ d的表达式如等于24则输出计算形如( a @ b ) @ ( c @ d ) 的表达式如等于24则输出计算形如( a @ b ) @ c ) @ d 的表达式如等于24则输出结束循环3个运算符循环3个运算符循环final中的全部排列Next i把result存入finalYN检验result(i,0)标志是否为1For i=1 to t&font color=#0556A3&参考文献：&/font&北京市第四中学网站
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1.75亿学生的选择
算24点：10、9、7、9 3、1、12、11 13、1、4、11 8、9、10、11 6、8、13、7
楼主你好：10、9、7、9：电脑无解 3、1、12、11：1:
(3 × (1 + 11) - 122:
3 × (1 + 11) - 123:
3 × 12 -(1 + 11)4:
(3 × 12) - (1 + 11)5:
3 × 12 - 1 - 116:
(3 × 12) - 1 - 117:
(3 × 12 - 1) - 118:
(3 × 12) - 1) - 119:
3 × 12 -(11 + 1)10:
(3 × 12) - (11 + 1)11:
3 × 12 - 11 - 112:
(3 × 12) - 11 - 113:
(3 × 12 - 11) - 114:
(3 × 12) - 11) - 115:
(3 × (11 + 1)) - 1216:
3 × (11 + 1) - 1217:
(1 + 11) × 3 - 1218:
(1 + 11) × 3) - 1219:
12 × 3 -(1 + 11)20:
(12 × 3) - (1 + 11)21:
12 × 3 - 1 - 1122:
(12 × 3) - 1 - 1123:
(12 × 3 - 1) - 1124:
(12 × 3) - 1) - 1125:
12 × 3 -(11 + 1)26:
(12 × 3) - (11 + 1)27:
12 × 3 - 11 - 128:
(12 × 3) - 11 - 129:
(12 × 3 - 11) - 130:
(12 × 3) - 11) - 131:
(11 + 1) × 3 - 1232:
(11 + 1) × 3) – 1213.1.4.11：电脑无解8.9.10.11：电脑无解6.8.13.7：电脑无解 
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3*12-(11+1)=24
【楼主好！~我来抢个位置！】这是此女的白痴话、、可以省略不看、、
10-(3×-6+4)=24 10-3×-6-4=24 10-(4+3×-6)=24 10-4-3×-6=24 (10-4)×3--6=24 (10+4+-6)×3=24 10-(4+-6×3)=24 10-4--6×3...
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