Solution #1:  12-1-2-3-4-7-10-9-8-5-6-11

 

Solution #2:  12-1-2-3-4-9-10-7-6-5-8-11

 

 

The following Visual Basic program found these results in less than a second.

 

Imports System
Imports System.IO
Imports System.Text
Imports System.Runtime.InteropServices
Imports System.Math
Module Module1
    Sub Main()
        Randomize()
        Dim strstarttime As String
        Dim strendtime As String
        Dim strend As String
        Dim intclock(12) As Integer
        strstarttime = TimeOfDay
        Console.WriteLine("Start of execution: " & strstarttime)
        intclock(0) = 12
        intclock(1) = 1
        intclock(2) = 2
        intclock(3) = 3
        intclock(4) = 4
        intclock(5) = 5
        intclock(6) = 6
        intclock(7) = 7
        intclock(8) = 8
        intclock(9) = 9
        intclock(10) = 10
        intclock(11) = 11
        For indexa As Integer = 0 To 11
            sixnumbers(indexa, intclock)
        Next
        strendtime = TimeOfDay
        Console.WriteLine(" ")
        Console.WriteLine("Start of execution: " & strstarttime)
        strendtime = TimeOfDay
        Console.WriteLine("End of execution: " & strendtime)
        strend = "?"
        Console.WriteLine(" ")
        While strend <> "X"
            Console.WriteLine("Please enter X to exit program...")
            strend = UCase(Console.ReadLine())
        End While
    End Sub

    Sub sixnumbers(ByRef indexa, ByRef intclock)
        Dim intsub1 As Integer
        Dim intsub2 As Integer
        Dim int6hours(6) As Integer
        intsub1 = 0
        For indexb As Integer = indexa To indexa + 5
            intsub2 = indexb Mod 12
            int6hours(intsub1) = intclock(intsub2)
            intsub1 += 1
        Next
        For index1 As Integer = 0 To 5
            For index2 As Integer = 0 To 5
                If index2 <> index1 Then
                    For index3 As Integer = 0 To 5
                        If index3 <> index1 And _
                        index3 <> index2 Then
                            For index4 As Integer = 0 To 5
                                If index4 <> index1 And _
                                index4 <> index2 And _
                                index4 <> index3 Then
                                    For index5 As Integer = 0 To 5
                                        If index5 <> index1 And _
                                        index5 <> index2 And _
                                        index5 <> index3 And _
                                        index5 <> index4 Then
                                            For index6 As Integer = 0 To 5
                                                If index6 <> index1 And _
                                                index6 <> index2 And _
                                                index6 <> index3 And _
                                                index6 <> index4 And _
                                                index6 <> index5 Then
                                                    adjustclock(indexa, _
                                                    index1, _
                                                    index2, _
                                                    index3, _
                                                    index4, _
                                                    index5, _
                                                    index6, _
                                                    intclock, _
                                                    int6hours)
                                                End If
                                            Next
                                        End If
                                    Next
                                End If
                            Next
                        End If
                    Next
                End If
            Next
        Next
    End Sub

    Sub adjustclock(ByRef indexa, _
    ByRef index1, _
    ByRef index2, _
    ByRef index3, _
    ByRef index4, _
    ByRef index5, _
    ByRef index6, _
    ByRef intclock, _
    ByRef int6hours)
        Dim intnewclock(12) As Integer
        Dim intnew6hours(6) As Integer
        Dim intsub1 As Integer
        Dim intsub2 As Integer
        Dim intsum As Integer
        Dim strprime As String
        For indexb As Integer = 0 To 11
            intnewclock(indexb) = intclock(indexb)
        Next
        intnew6hours(0) = int6hours(index1)
        intnew6hours(1) = int6hours(index2)
        intnew6hours(2) = int6hours(index3)
        intnew6hours(3) = int6hours(index4)
        intnew6hours(4) = int6hours(index5)
        intnew6hours(5) = int6hours(index6)
        intsub1 = indexa
        For indexb As Integer = 0 To 5
            intnewclock(intsub1) = intnew6hours(indexb)
            intsub1 += 1
            intsub1 = intsub1 Mod 12
        Next
        strprime = "y"
        For indexb As Integer = 0 To 11
            intsub2 = indexb + 1
            intsub2 = intsub2 Mod 12
            intsum = intnewclock(indexb) + intnewclock(intsub2)
            If intsum <> 3 And intsum <> 5 And intsum <> 7 And _
            intsum <> 11 And intsum <> 13 And intsum <> 17 And _
            intsum <> 19 And intsum <> 23 Then
                strprime = "n"
                Exit For
            End If
        Next
        If strprime = "y" Then
            Console.WriteLine("Here is such a clock:")
            For indexb As Integer = 0 To 11
                Console.WriteLine( _
                Str(intnewclock(indexb)))
            Next
        End If
    End Sub
End Module