Place the numbers 1 to 9 once in each row, column, long diagonal (marked with a heavy dot) and every 3x3 grid.

The 'cage' inclusions (individually coloured regions) indicate the sum or the product of the numbers in those cells.

Unlike Killer Sudoku, the same number may appear more than once in a cage. So, 36x in a cage which overlaps the 3x3 grids may contain two 6s and a 1.


My inspiration for this puzzle came from a variety of puzzles posted by Pete and Will at http://sudexel.com/forum/index.php

My thanks goes to brianjn for his hard work in producing the graphic.

(In reply to re(2): Solution by brianjn)

No problem. It's too long for exact quotation, but I can summarize the redundant parts. It executed in a reasonable amount of time, about 45 minutes to cover all possibilities. A better programmer would have done a more efficient job.

Here it is.

Imports System
Imports System.IO
Imports System.Text
Imports System.Runtime.InteropServices
Imports System.Math
Module Module1

    Dim matrix(0 To 8, 0 To 8) As Integer
    Dim error_flag As Boolean
    Dim solution_count As Integer = 0
    Dim sub0 As Integer
    Dim sub1 As Integer
    Dim work0 As Integer

    Dim start0 As Integer
    Dim end0 As Integer
    Dim start1 As Integer
    Dim end1 As Integer

    Dim starttime As String

Sub Main()
        Randomize()

'  Commented out, 1-time execution:

' generate_code()
' end

        starttime = TimeOfDay

        Console.WriteLine("Start execution: " & starttime)

        cell_00()

        Console.WriteLine(" ")
        Console.WriteLine("Start execution: " & starttime)
        Console.WriteLine("End execution: " & TimeOfDay)
        Console.ReadLine()

End Sub

(The code for subroutines "cell_00()" through "cell_88()" were also produced by computer program, then manually copy/pasted into the source. This was to eliminate the possibility of careless typos. I have never managed to get recursive code to work, so automated code generation was the next best thing.)     

Sub cell_00()
    For index0 As Integer = 1 To 9
            sub0 = 0
            sub1 = 0
            matrix(0, 0) = index0
            validity_checks()
            If error_flag = False Then
                cell_01()
            End If
        Next
End Sub
   
Sub cell_01()...

...etc. etc...

Sub cell_88()
        For index0 As Integer = 1 To 9
            sub0 = 8
            sub1 = 8
            matrix(8, 8) = index0
            validity_checks()
            If error_flag = False Then
                write_the_matrix()
            End If
        Next

End Sub

Sub validity_checks()

        Dim string0 As String

        error_flag = False

        For index0 As Integer = 0 To 8
            For index1 As Integer = 0 To 8
                If (index0 > sub0) Or _
                (index0 = sub0 And index1 > sub1) Then
                    matrix(index0, index1) = 999
                End If
            Next
        Next

        arithmetic_checks()
        If error_flag = True Then
            Exit Sub
        End If

        row_check()
        If error_flag = True Then
            Exit Sub
        End If

        column_check()
        If error_flag = True Then
            Exit Sub
        End If

        grid_3x3_check()
        If error_flag = True Then
            Exit Sub
        End If

        long_diagonal_0_check()
        If error_flag = True Then
            Exit Sub
        End If

        long_diagonal_1_check()
        If error_flag = True Then
            Exit Sub
        End If

        cage_checks()
        If error_flag = True Then
            Exit Sub
        End If

End Sub

Sub arithmetic_checks()
        Dim workm As Integer
        workm = matrix(sub0, sub1)

        ' 80x
        If sub0 = 0 Then
            If sub1 = 3 Or sub1 = 4 Or sub1 = 5 Then
                If (80 Mod workm) <> 0 Then
                    error_flag = True
                    Exit Sub
                End If
            End If
        End If

        ' 56x
        If sub0 = 0 Then
            If sub1 = 8 Then
                If (56 Mod workm) <> 0 Then
                    error_flag = True
                    Exit Sub
                End If
            End If
        End If
        If sub0 = 1 Then
            If sub1 = 7 Or sub1 = 8 Then
                If (56 Mod workm) <> 0 Then
                    error_flag = True
                    Exit Sub
                End If
            End If
        End If

        ...etc. etc. for all the other cages...
       
        ' 540x
        If sub0 = 6 Then
            If sub1 = 8 Then
                If (540 Mod workm) <> 0 Then
                    error_flag = True
                    Exit Sub
                End If
            End If
        End If
        If sub0 = 7 Then
            If sub1 = 7 Or sub1 = 8 Then
                If (540 Mod workm) <> 0 Then
                    error_flag = True
                    Exit Sub
                End If
            End If
        End If
        If sub0 = 8 Then
            If sub1 = 8 Then
                If (540 Mod workm) <> 0 Then
                    error_flag = True
                    Exit Sub
                End If
            End If
        End If

End Sub

Sub row_check()
        For index1 As Integer = 0 To 8
            If index1 <> sub1 Then
                If matrix(sub0, sub1) = matrix(sub0, index1) Then
                    error_flag = True
                End If
            End If
        Next
End Sub

Sub column_check()
        For index0 As Integer = 0 To 8
            If index0 <> sub0 Then
                If matrix(sub0, sub1) = matrix(index0, sub1) Then
                    error_flag = True
                End If
            End If
        Next
End Sub

Sub grid_3x3_check()

        start0 = 0
        end0 = 2

        start1 = 0
        end1 = 2
        check_grid()
        If error_flag = True Then
            Exit Sub
        End If

...etc. etc. for the other grids...       

        start1 = 0
        end1 = 2
        check_grid()
        If error_flag = True Then
            Exit Sub
        End If
        start1 = 3
        end1 = 5
        check_grid()
        If error_flag = True Then
            Exit Sub
        End If
        start1 = 6
        end1 = 8
        check_grid()
        If error_flag = True Then
            Exit Sub
        End If

End Sub
   
Sub check_grid()
        For index0 As Integer = start0 To end0
            For index1 As Integer = start1 To end1
                If matrix(index0, index1) <= 9 Then
                    For index00 As Integer = start0 To end0
                        For index11 As Integer = start1 To end1
                            If index0 <> index00 Or index1 <> index11 Then
                                If matrix(index0, index1) = matrix(index00, index11) Then
                                    error_flag = True
                                End If
                            End If
                        Next
                    Next
                End If
            Next
        Next
End Sub

Sub long_diagonal_0_check()
        For index0 As Integer = 0 To 8
            If matrix(index0, index0) <= 9 Then
                For index1 As Integer = 0 To 8
                    If index1 <> index0 Then
                        If matrix(index0, index0) = matrix(index1, index1) Then
                            error_flag = True
                        End If
                    End If
                Next
            End If
        Next
End Sub

Sub long_diagonal_1_check()
        For index0 As Integer = 0 To 8
            If matrix(index0, 8 - index0) <= 9 Then
                For index1 As Integer = 0 To 8
                    If index1 <> index0 Then
                        If matrix(index0, 8 - index0) = matrix(index1, 8 - index1) Then
                            error_flag = True
                        End If
                    End If
                Next
            End If
        Next
End Sub

Sub cage_checks()

        If matrix(0, 5) <= 9 Then
            work0 = matrix(0, 3) * matrix(0, 4) * matrix(0, 5)
            If work0 <> 80 Then
                error_flag = True
                Exit Sub
            End If
        End If

...etc. etc. for the other cages...

        If matrix(8, 8) <= 9 Then
            work0 = matrix(6, 8) * matrix(7, 7) * matrix(7, 8) * matrix(8, 8)
            If work0 <> 540 Then
                error_flag = True
                Exit Sub
            End If
        End If

End Sub

Sub write_the_matrix()
        Dim objStreamWriter As StreamWriter
        Dim string0 As String
        objStreamWriter = _
        New StreamWriter("my file id - Perplexus has problems with backslashes...")

        solution_count += 1

        string0 = solution_count & " solutions found."
        objStreamWriter.WriteLine(string0)
        string0 = "----------------------------"
        objStreamWriter.WriteLine(string0)
        For index0 As Integer = 0 To 8
            string0 = ""
            For index1 As Integer = 0 To 8
                string0 &= matrix(index0, index1) & " "
            Next
            objStreamWriter.WriteLine(string0)
        Next
        string0 = "----------------------------"
        objStreamWriter.WriteLine(string0)
        objStreamWriter.Flush()
        objStreamWriter.Close()

End Sub

' One-time code generator...

Sub generate_code()
        Dim objStreamWriter As StreamWriter
        Dim string0 As String
        objStreamWriter = _
        New StreamWriter("my file id")
        For index0 As Integer = 0 To 8
            For index1 As Integer = 0 To 8
                string0 = _
                "Sub cell_" & index0 & index1 & "()"
                objStreamWriter.WriteLine(string0)
                string0 = _
                "For index0 as Integer = 1 to 9"
                objStreamWriter.WriteLine(string0)
                string0 = _
                "sub0 = " & index0
                objStreamWriter.WriteLine(string0)
                string0 = _
                "sub1 = " & index1
                objStreamWriter.WriteLine(string0)
                string0 = "matrix(" & index0 & ", " & index1 & ") = index0"
                objStreamWriter.WriteLine(string0)
                string0 = _
                "validity_checks()"
                objStreamWriter.WriteLine(string0)
                string0 = _
                "If error_flag = False Then"
                objStreamWriter.WriteLine(string0)
                If index1 < 8 Then
                    string0 = _
                    "cell_" & index0 & index1 + 1 & "()"
                ElseIf index0 < 8 Then
                    string0 = _
                    "cell_" & index0 + 1 & "0()"
                Else
                    string0 = "write_the_matrix()"
                End If
                objStreamWriter.WriteLine(string0)
                string0 = "End If"
                objStreamWriter.WriteLine(string0)
                string0 = "Next"
                objStreamWriter.WriteLine(string0)
                string0 = "End Sub"
                objStreamWriter.WriteLine(string0)
            Next
        Next

        objStreamWriter.Flush()
        objStreamWriter.Close()

End Sub

End Module

 

Edited on May 28, 2008, 8:14 am

Posted by Penny on 2008-05-28 07:58:02