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分享朋友提了个智力问题，苦想后无解，请大家帮忙！
题目如下：有十二个球，其中一个重量不同，其余十一个重量相同，个一部天平，只许称三次，请找出不同的一个！~！
这个题的难点在重量不同的那个球不知道是轻是重，请大家帮忙想想看。（如果有兴趣的话可以用vb写个算法小程序发上来）
这个题的难点在重量不同的那个球不知道是轻是重，请大家帮忙想想看。（如果有兴趣的话可以用vb写个算法小程序发上来）
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XmagicX 2004-04-13
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不知道重量,光是比较不等的情况,就至少是4步了
二师兄的老公 2004-04-13
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看了小马哥的链接，汗！
richboy2003 2004-04-13
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alicky(周松) :你的还是错的，错在第2步！如果那个不同重量的球是轻的，你第2次称天平就是平横的，你还有一步了。你只知道轻球在那6个球里！你仔细想想
yoki 2004-04-13
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http://www.trucy.net/cgi-bin/forum/view.cgi?forum=6&topic=17
pigpag 2004-04-13
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听说是某个公司的招聘题目。还要对球进行编号，非常麻烦。楼上说的方法不正确，因为那个特殊的球也可能比普通球轻。
cigoner 2004-04-13
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需要多称一次吧。。。想不出办法~
Alicky 2004-04-13
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随便再说一下，这个是用不着写程序的，要实践。如果你还不懂的话，给我信息。
Alicky 2004-04-13
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第一次称：把十二个球分成两份，天平一边一份，重的那六个球拿出来。
第二次称：把第一次称出来的六个球再分成两份，天平一边一份，重的那三个球再拿出来。
第三次称：再第三次拿出来的三个球中，随便拿两个出来称，如果天平两边一样重，说明剩下的那个就是你要找的，如果天平两边不一样重的话，那个重的就是你要找的。这一步是关键，你仔细想想。
第二次称：把第一次称出来的六个球再分成两份，天平一边一份，重的那三个球再拿出来。
第三次称：再第三次拿出来的三个球中，随便拿两个出来称，如果天平两边一样重，说明剩下的那个就是你要找的，如果天平两边不一样重的话，那个重的就是你要找的。这一步是关键，你仔细想想。
cityou 2004-04-13
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以前有人问过我这个问题，我也一直没整明白……
cityou 2004-04-13
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用一次称其中两份不能知道不同的球在哪一堆里。a,b,c三堆，如果a,b称称平，那么c里有一个不同；但ab不平呢？a里有不同还是b里有不同？
richboy2003 2004-04-13
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"先将小球分成三份，秤其中的两份可以知道重量不同的球在那一份中"----第一步就错的！说了不知道重量不同的球是轻还是重。天平不平，你知道重量不同的球在那一份中？-----作为程序员你的想法也太简单了，搞笑
GERY2003 2004-04-13
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先将小球分成三份，秤其中的两份可以知道重量不同的球在那一份中
从那一份取出两个秤一下，如果重量相同，那么球就在剩下的那两个中
再从剩下的两个当中取一个，与刚才秤的两个球的其中一个再秤，就能知道
重量不同的球球是那个
从那一份取出两个秤一下，如果重量相同，那么球就在剩下的那两个中
再从剩下的两个当中取一个，与刚才秤的两个球的其中一个再秤，就能知道
重量不同的球球是那个
zhangsunphone 2004-04-13
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这个问题以前看过了，方法很多啊。
paocai2003 2004-04-13
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分析的非常完整,谢谢 northwolves(野性的呼唤),也谢谢作者.供我学习参考.
UP!
UP!
northwolves 2004-04-13
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3步可以实现（中午没事刚写出来）：
Private Sub Command1_Click()
Dim x(1 To 12) As String, temp As Integer, i As Integer
For i = 1 To 12
x(i) = 2
Next
Randomize
temp = (Int(Rnd * 12 + 1))
x(temp) = 2 + (-1) ^ Int(Rnd * 2) ' define a light ball
getit x
End Sub
Sub getit(ByRef x() As String)
Dim a(1 To 12) As Double, i As Long, heavy As Boolean, diff As Integer
For i = 1 To 12
a(i) = CDbl(x(i))
Next
If a(1) + a(2) + a(3) + a(4) = a(5) + a(6) + a(7) + a(8) Then ' step 1
If a(9) + a(10) = a(11) + a(1) Then ' step 2
diff = 12
If a(1) > a(12) Then 'step 3
heavy = False
Else
heavy = True
End If
End If
If a(9) + a(10) > a(11) + a(1) Then ' step 2
If a(9) = a(10) Then 'step 3
diff = 11
heavy = False
ElseIf a(9) > a(10) Then 'step 3
diff = 9
heavy = True
ElseIf a(9) < a(10) Then 'step 3
diff = 10
heavy = True
End If
End If
If a(9) + a(10) < a(11) + a(1) Then 'step 2
If a(9) = a(10) Then 'step 3
diff = 11
heavy = True
ElseIf a(9) > a(10) Then 'step 3
diff = 10
heavy = False
ElseIf a(9) < a(10) Then 'step 3
diff = 9
heavy = False
End If
End If
End If
If a(1) + a(2) + a(3) + a(4) > a(5) + a(6) + a(7) + a(8) Then 'step 1
If a(1) + a(6) + a(7) + a(8) = a(5) + a(9) + a(10) + a(11) Then 'step 2
If a(2) = a(3) Then diff = 4 'step 3
If a(2) < a(3) Then diff = 3 'step 3
If a(2) > a(3) Then diff = 2 'step 3
heavy = True
End If
If a(1) + a(6) + a(7) + a(8) > a(5) + a(9) + a(10) + a(11) Then 'step 2
If a(1) = a(2) Then 'step 3
diff = 5
heavy = False
End If
If a(1) > a(2) Then 'step 3
diff = 1
heavy = True
End If
End If
If a(1) + a(6) + a(7) + a(8) < a(5) + a(9) + a(10) + a(11) Then 'step 2
If a(6) = a(7) Then 'step 3
diff = 8
End If
If a(6) > a(7) Then 'step 3
diff = 7
End If
If a(6) < a(7) Then 'step 3
diff = 6
End If
heavy = False
End If
End If
If a(1) + a(2) + a(3) + a(4) < a(5) + a(6) + a(7) + a(8) Then 'step 1
If a(1) + a(6) + a(7) + a(8) = a(5) + a(9) + a(10) + a(11) Then 'step 2
If a(2) = a(3) Then 'step 3
diff = 4
End If
If a(2) < a(3) Then 'step 3
diff = 2
End If
If a(2) > a(3) Then 'step 3
diff = 3
End If
heavy = False
End If
If a(1) + a(6) + a(7) + a(8) > a(5) + a(9) + a(10) + a(11) Then 'step 2
If a(6) = a(7) Then diff = 8 'step 3
If a(6) > a(7) Then diff = 6 'step 3
If a(6) < a(7) Then diff = 7 'step 3
heavy = True
End If
If a(1) + a(6) + a(7) + a(8) < a(5) + a(9) + a(10) + a(11) Then 'step 2
If a(1) = a(2) Then 'step 3
diff = 5
heavy = True
End If
If a(1) < a(2) Then 'step 3
diff = 1
heavy = False
End If
End If
End If
MsgBox "若12个球重量为：" & Join(x, ",") & vbCrLf & vbCrLf & "则第 " & diff & "个球偏" & IIf(heavy = True, "重！", "轻！"), 64, "结果"
End Sub
Private Sub Command1_Click()
Dim x(1 To 12) As String, temp As Integer, i As Integer
For i = 1 To 12
x(i) = 2
Next
Randomize
temp = (Int(Rnd * 12 + 1))
x(temp) = 2 + (-1) ^ Int(Rnd * 2) ' define a light ball
getit x
End Sub
Sub getit(ByRef x() As String)
Dim a(1 To 12) As Double, i As Long, heavy As Boolean, diff As Integer
For i = 1 To 12
a(i) = CDbl(x(i))
Next
If a(1) + a(2) + a(3) + a(4) = a(5) + a(6) + a(7) + a(8) Then ' step 1
If a(9) + a(10) = a(11) + a(1) Then ' step 2
diff = 12
If a(1) > a(12) Then 'step 3
heavy = False
Else
heavy = True
End If
End If
If a(9) + a(10) > a(11) + a(1) Then ' step 2
If a(9) = a(10) Then 'step 3
diff = 11
heavy = False
ElseIf a(9) > a(10) Then 'step 3
diff = 9
heavy = True
ElseIf a(9) < a(10) Then 'step 3
diff = 10
heavy = True
End If
End If
If a(9) + a(10) < a(11) + a(1) Then 'step 2
If a(9) = a(10) Then 'step 3
diff = 11
heavy = True
ElseIf a(9) > a(10) Then 'step 3
diff = 10
heavy = False
ElseIf a(9) < a(10) Then 'step 3
diff = 9
heavy = False
End If
End If
End If
If a(1) + a(2) + a(3) + a(4) > a(5) + a(6) + a(7) + a(8) Then 'step 1
If a(1) + a(6) + a(7) + a(8) = a(5) + a(9) + a(10) + a(11) Then 'step 2
If a(2) = a(3) Then diff = 4 'step 3
If a(2) < a(3) Then diff = 3 'step 3
If a(2) > a(3) Then diff = 2 'step 3
heavy = True
End If
If a(1) + a(6) + a(7) + a(8) > a(5) + a(9) + a(10) + a(11) Then 'step 2
If a(1) = a(2) Then 'step 3
diff = 5
heavy = False
End If
If a(1) > a(2) Then 'step 3
diff = 1
heavy = True
End If
End If
If a(1) + a(6) + a(7) + a(8) < a(5) + a(9) + a(10) + a(11) Then 'step 2
If a(6) = a(7) Then 'step 3
diff = 8
End If
If a(6) > a(7) Then 'step 3
diff = 7
End If
If a(6) < a(7) Then 'step 3
diff = 6
End If
heavy = False
End If
End If
If a(1) + a(2) + a(3) + a(4) < a(5) + a(6) + a(7) + a(8) Then 'step 1
If a(1) + a(6) + a(7) + a(8) = a(5) + a(9) + a(10) + a(11) Then 'step 2
If a(2) = a(3) Then 'step 3
diff = 4
End If
If a(2) < a(3) Then 'step 3
diff = 2
End If
If a(2) > a(3) Then 'step 3
diff = 3
End If
heavy = False
End If
If a(1) + a(6) + a(7) + a(8) > a(5) + a(9) + a(10) + a(11) Then 'step 2
If a(6) = a(7) Then diff = 8 'step 3
If a(6) > a(7) Then diff = 6 'step 3
If a(6) < a(7) Then diff = 7 'step 3
heavy = True
End If
If a(1) + a(6) + a(7) + a(8) < a(5) + a(9) + a(10) + a(11) Then 'step 2
If a(1) = a(2) Then 'step 3
diff = 5
heavy = True
End If
If a(1) < a(2) Then 'step 3
diff = 1
heavy = False
End If
End If
End If
MsgBox "若12个球重量为：" & Join(x, ",") & vbCrLf & vbCrLf & "则第 " & diff & "个球偏" & IIf(heavy = True, "重！", "轻！"), 64, "结果"
End Sub
