找鸡蛋：一个智力题的编程求解解决办法

找鸡蛋：一个智力题的编程求解
有12个鸡蛋，其中有一个和其他不一样重（或重或轻），给你一个天平，只准你称3次，然后找出那个和其他不一样重的鸡蛋。并且知道它是比其他重还是比其他轻！ 

我想了半天，没想出来，感觉去上网查或问别人太没劲，就想着是否可以用搜索穷举出结果，我初步的想法是：
1 测试数据集 12
2 数据表示 composite 比较
3 行为集： 比较，剪枝，添加，判断，分组 
4 规则：满足 与否
穷举各种分组策略，记录行为轨迹，对成功的，在其他11组上验证。
关键是行为集的定义 
现在向大家求教，望不吝赐教！

------解决方案--------------------
等看了答案就知道穷举法根本不可行
建议看看答案吧，看完答案能编出算法就不简单

------解决方案--------------------
用递归的方法还是很容易实现的。
思路定好了，用什么语言都很容易实现。
比如说VB的代码就可以这样写：

Option Explicit

Private Sub cmdEgg12_Click()
Dim i As Long
Dim iMin As Long
Dim iMax As Long

Dim j As Long
Dim jMin As Long
Dim jMax As Long

Dim k As Long

Dim arrData() As Long

iMin = 0
iMax = 11
ReDim arrData(iMax)
For i = iMin To iMax
arrData(i) = 100
Next i
arrData(4) = 90
'arrData(7) = 110

jMin = iMin
jMax = Fix(iMax / 2)

Debug.Print vbCrLf
k = EggOut(arrData(), iMin, iMax, jMin, jMax)

Debug.Print "* " & iMin & "; " & iMax & "; " & jMin & "; " & jMax & "; " & k
End Sub


Private Function EggOut( _
arrData() As Long, _
ByRef iMin As Long, _
ByRef iMax As Long, _
ByRef jMin As Long, _
ByRef jMax As Long _
) As Long

Dim lngSum As Long

lngSum = 0

'' Sum it
lngSum = EggSum(arrData(), jMin, jMax)

Debug.Print "* " & jMin & " " & jMax & " " & lngSum

'' Same data?
If lngSum = ((jMax - jMin + 1) * 100) Then
iMin = jMax + 1
iMax = iMax

jMin = iMin
jMax = jMin + Fix((iMax - jMin) / 2)
'' Not the same?
Else
iMin = iMin
iMax = jMax

jMin = iMin
jMax = jMin + Fix((iMax - jMin) / 2)
End If

'' Continue?
If ((jMax - jMin) <> 1) Then
EggOut = EggOut(arrData(), iMin, iMax, jMin, jMax)
Else
'' Result
Debug.Print "*Result* " & jMin & " " & jMax & " " & lngSum
Debug.Print "*Result* " & jMin & " " & arrData(jMin) & "; " & jMin + 1 & " " & arrData(jMin + 1) & "; " & jMin + 2 & " " & arrData(jMin + 2)
End If
End Function


Private Function EggSum( _
arrData() As Long, _
iMin As Long, _
iMax As Long _
) As Long

Dim i As Long

Dim lngSum As Long

lngSum = 0
For i = iMin To iMax
lngSum = lngSum + arrData(i)
Next i

EggSum = lngSum
End Function

------解决方案--------------------
如果想优化一下，那就写成这样：

Option Explicit

Private Sub cmdEgg12_Click()
Dim i As Long
Dim iMin As Long
Dim iMax As Long

Dim j As Long
Dim jMin As Long
Dim jMax As Long

Dim k As Long

Dim arrData() As Long

iMin = 0
iMax = 11
ReDim arrData(iMax)
For i = iMin To iMax
arrData(i) = 100
Next i
arrData(4) = 90
'arrData(7) = 110

'' Check ranage