題目：
請將123456789九個數字以特定的順序排列，組成一個9位數ABCDEFGHI（每個數字只能使用一次），使得：
1.第一位數字組成的整數可以被1整除
2.第一、二位數字組成的整數可以被2整除
3.第一、二、三位數字組成的整數可以被3整除
4.第一、二、三、四位數字組成的整數可以被4整除
......
9.第一、二、三...九位數字組成的整數可以被9整除
分析：
通常想法是遍歷9！=362280種排列。
其實第5位E一定是5，這樣可縮減到8!=40320種排列
進一步分析，偶數位一定是偶數（BDFH={2，4，6，8}），奇數位一定是奇數（ACGI={1，3，7，9}），因而只需分析P(4,4)*P(4,4)=576種排列。
繼續分析，4能整除 10*C+D，故D=2 或 6, 加之8能整除 10*G+H，故D,H={2，6}，所以B，F={4，8}，故需分析P(4,4)*P(2,2)*P(2,2)=48種排列
接着分析，3 能整除 100* D+ 10 * 5+ F，所以DEF={258 ，654}，ABC，GHI能被3整除
如果DEF=258，則，ABC={147，741}，GHI={369，963}，但1472589，7412589均不能被7整除，不符合條件，故DEF=654，
B=8，H=2.此時只有P(4,4)=24種排列
又7能整除A8C654G，故7整除（A+4C+G）,而G={3，7}，如果G=3，ABC爲{189，789，981，987}均不滿足條件，故G=7，此時ABC={183，189，381，981}中只有381符合條件，故ABCDEFGHI=381654729
此時如果需要寫代碼，一句就夠了：
Debug.print 381654729
附幾種解法：
由yier_fang 提供
- Sub cnft()
- '定義一個數組
- Dim a
- '定義字符串
- Dim strNums As String
- strNums = "1,2,3,4,5,6,7,8,9"
- '開始循環
- Dim i, j, k As Integer
- For i = 2 To 9
- a = Split(strNums, ",")
- strNums = ""
- For k = 0 To UBound(a)
- For j = 1 To 9
- If (a(k) & j) Mod i = 0 Then
- If InStr(a(k), j) = 0 Then
- strNums = strNums & "," & a(k) & j
- End If
- End If
- Next j
- Next k
- strNums = Right(strNums, Len(strNums) - 1)
- Next i
- Erase a
- MsgBox ("運行結果爲:" & strNums)
- End Sub
代碼2：
- Sub Getit()
- Dim a, b, c, d, e, f, g, h, i As Integer, num1, num2 As String, x As Double
- e = 5: num1 = "123456789": num2 = "此數爲：": t = Timer
- For a = 1 To 9 Step 2
- If a = e Then GoTo 10
- For b = 2 To 8 Step 2
- For c = 1 To 9 Step 2
- x = a + b + c
- If c = a Or c = e Or Int(x / 3) <> x / 3 Then GoTo 30
- For d = 2 To 8 Step 2
- x = 10 * c + d
- If d = b Or Int(x / 4) <> x / 4 Then GoTo 40
- For f = 2 To 8 Step 2
- x = d + e + f
- If f = b Or f = d Or Int(x / 3) <> x / 3 Then GoTo 60
- For g = 1 To 9 Step 2
- x = a * 1000000 + b * 100000 + c * 10000 + d * 1000 + e * 100 + f * 10 + g
- If g = a Or g = c Or g = e Or Int(x / 7) <> x / 7 Then GoTo 70
- For h = 2 To 8 Step 2
- x = 10 * g + h
- If h = b Or h = d Or h = f Or Int(x / 8) <> x / 8 Then GoTo 80
- For i = 1 To 9 Step 2
- If i = a Or i = c Or i = e Or i = g Then GoTo 90
- num2 = num2 + Mid(num1, a, 1) + Mid(num1, b, 1) + Mid(num1, c, 1)
- num2 = num2 + Mid(num1, d, 1) + Mid(num1, e, 1) + Mid(num1, f, 1)
- num2 = num2 + Mid(num1, g, 1) + Mid(num1, h, 1) + Mid(num1, i, 1)
- num2 = num2 + Chr(13) + Chr(10) + "計算時間：" + Str(Timer - t) + "秒"
- MsgBox (num2)
- 90:
- Next i
- 80:
- Next h
- 70:
- Next g
- 60:
- Next f
- 40:
- Next d
- 30:
- Next c
- 20:
- Next b
- 10:
- Next a
- End Sub
代碼3
（彭希仁 提供）
- Dim x, s As String
- Sub cai()
- Call caii("", 0)
- MsgBox s
- End Sub
- Sub caii(a, i)
- For j = 1 To 9
- If Not (a Like "*" & j & "*") And (a & j) Mod (i + 1) = 0 Then
- If i + 1 = 9 Then
- s = s & a & j & vbCrLf
- Else
- Call caii(a & j, i + 1)
- End If
- End If
- Next j
- End Sub
代碼4：
- Sub cnft()
- getNum
- End Sub
- Sub getNum(Optional ByRef strNums As String = "", Optional ByRef iTurn As Integer = 1)
- Dim i As Integer, tm As Single
- tm = Timer
- For i = 1 To 9
- If InStr(strNums, i) = 0 Then
- If (strNums & i) Mod iTurn = 0 Then
- If iTurn = 9 Then
- MsgBox strNums & i & vbCrLf & "用時:" & Timer - tm & "秒"
- Else
- Call getNum(strNums & i, iTurn + 1)
- End If
- End If
- End If
- Next i
- End Sub
代碼5
- Sub macro1()
- Dim d, s, x, i As Long, j As Long, n As Currency, k As Long, befit As Boolean
- d = Array(1, 3, 7, 9)
- s = Array(2, 4, 6, 8)
- x = Split("0123 0132 0213 0231 0312 0321 1023 1032 1203 1230 1302 1320 2013 2031 2103 2130 2301 2310 3012 3021 3102 3120 3201 3210")
- For i = 0 To 23
- For j = 0 To 23
- n = Val(d(Mid(x(i), 1, 1)) & s(Mid(x(j), 1, 1)) & d(Mid(x(i), 2, 1)) & s(Mid(x(j), 2, 1)) & 5 & s(Mid(x(j), 3, 1)) & d(Mid(x(i), 3, 1)) & s(Mid(x(j), 4, 1)) & d(Mid(x(i), 4, 1)))
- befit = True
- For k = 2 To 8
- If Not Left(n, k) Mod k = 0 Then befit = False: Exit For
- Next
- If befit = True Then Debug.Print n
- Next
- Next
- End Sub