Promising them an increase in their allowance if they get the answer, I offer my two sons, Peter and Paul, the following puzzler:

"I am thinking of a rectangle with integer sides, each of which are greater than one inch. The total perimeter of the rectangle is no greater than eighty inches."

I then whisper the total area to Peter and the total perimeter to Paul. Neither of them are allowed to tell the other what they heard: their job is to work out the rectangle's dimensions.

Their subsequent conversation goes like this:

Peter: Hmmm... I have no idea what the perimeter is.
Paul: I knew you were going to say that. However, I don't know what the area is.
Peter: Still no clue as to the perimeter...
Paul: But now I know what the area is!
Peter: And I know what the perimeter is!

What are the dimensions of the rectangle?

(In reply to Various comments (spoilers!) by nikki)

[Sorry, I wasn't being sarcastic. You were right all along in the sense that you picked up right away on Paul's  subtle first statement, although your first answer was not correct. Remember my comment: "I may be stumbling over that subtle hint 'I knew you were going to say that' by Paul" ? At least I was right about that.]

You were quick to see what eluded me. My original program was not taking that subtle initial remark by Paul into account. When I changed Paul's initial crosscheck to exclude any perimeter which maps to any unique area, I get the answer you get:

perimeter = 22, area = 30.

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 intsize As Integer
        Dim inttabarea(0, 0) As Integer
        Dim inttabper(0, 0) As Integer
        Dim intloop1 As Integer = 0
        Dim intloop2 As Integer = 0
        Dim intmax As Integer = 0
        Dim strstring As String
        Dim strlit As String
        strstarttime = TimeOfDay
        Console.WriteLine("Start of execution: " & strstarttime)
        size_tables(intsize)
        ReDim inttabarea(intsize, intsize + 1)
        ReDim inttabper(intsize, intsize + 1)
        intloop1 = intsize - 1
        intloop2 = intsize
        gen_tables(inttabarea, inttabper, _
        intloop1, intloop2, intmax)
        intloop2 = intmax
        'Peter: Hmmm... I have no idea what the perimeter is.
        singletonpurge(inttabarea, intloop1, intloop2)
        'Paul: I knew you were going to say that. However, I    'don't know  what the area is.
        initialcrosscheck(inttabper, inttabarea, intloop1, intloop2)
        singletonpurge(inttabper, intloop1, intloop2)
        'Peter: Still no clue as to the perimeter...
        crosscheck(inttabarea, inttabper, intloop1, intloop2)
        singletonpurge(inttabarea, intloop1, intloop2)
        'Paul: But now I know what the area is!
        crosscheck(inttabper, inttabarea, intloop1, intloop2)
        multiplepurge(inttabper, intloop1, intloop2)
        'Peter: And I know what the perimeter is!
        crosscheck(inttabarea, inttabper, intloop1, intloop2)
        multiplepurge(inttabarea, intloop1, intloop2)
        write_answers(inttabarea, inttabper, intloop1, intloop2)
        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 singletonpurge(ByRef inttab, ByRef intloop1, ByRef intloop2)
        Dim intcount As Integer
        For index1 As Integer = 0 To intloop1
            intcount = 0
            For index2 As Integer = 0 To intloop2
                If inttab(index1, index2) <> 0 Then
                    intcount += 1
                End If
            Next
            If intcount < 3 Then
                For index2 As Integer = 0 To intloop2
                    inttab(index1, index2) = 0
                Next
            End If
        Next
    End Sub

    Sub multiplepurge(ByRef inttab, ByRef intloop1, ByRef intloop2)
        Dim intcount As Integer
        For index1 As Integer = 0 To intloop1
            intcount = 0
            For index2 As Integer = 0 To intloop2
                If inttab(index1, index2) <> 0 Then
                    intcount += 1
                End If
            Next
            If intcount <> 2 Then
                For index2 As Integer = 0 To intloop2
                    inttab(index1, index2) = 0
                Next
            End If
        Next
    End Sub

    Sub initialcrosscheck( _
    ByRef inttab1, ByRef inttab2, ByRef intloop1, ByRef intloop2)
        Dim intcount As Integer
        For index1 As Integer = 0 To intloop1
            For index2 As Integer = 1 To intloop2
                If inttab1(index1, index2) <> 0 Then
                    intcount = 0
                    For index3 As Integer = 0 To intloop1
                        If inttab1(index1, index2) = inttab2(index3, 0) Then
                            For index4 As Integer = 1 To intloop2
                                If inttab2(index3, index4) <> 0 Then
                                    intcount += 1
                                End If
                            Next
                            Exit For
                        End If
                    Next
                    If intcount <= 1 Then
                        For index5 As Integer = 0 To intloop2
                            inttab1(index1, index5) = 0
                        Next
                    End If
                End If
            Next
        Next
    End Sub

    Sub crosscheck( _
    ByRef inttab1, ByRef inttab2, ByRef intloop1, ByRef intloop2)
        Dim intcount As Integer
        For index1 As Integer = 0 To intloop1
            For index2 As Integer = 1 To intloop2
                If inttab1(index1, index2) <> 0 Then
                    intcount = 0
                    For index3 As Integer = 0 To intloop1
                        If inttab1(index1, index2) = inttab2(index3, 0) Then
                            intcount += 1
                            Exit For
                        End If
                    Next
                    If intcount = 0 Then
                        inttab1(index1, index2) = 0
                    End If
                End If
            Next
        Next
    End Sub

    Sub size_tables(ByRef intsize)
        intsize = 0
        For index1 As Integer = 2 To 80
            For index2 As Integer = index1 To 80
                If (2 * index1) + (2 * index2) <= 80 Then
                    intsize += 1
                End If
            Next
        Next
    End Sub

    Sub gen_tables(ByRef inttabarea, ByRef inttabper, _
    ByRef intloop1, ByRef intloop2, ByRef intmax)
        Dim intarea As Integer
        Dim intper As Integer
        For index1 As Integer = 0 To intloop1
            For index2 As Integer = 0 To intloop2
                inttabarea(index1, index2) = 0
                inttabper(index1, index2) = 0
            Next
        Next
        For index1 As Integer = 2 To 80
            For index2 As Integer = index1 To 80
                If (2 * index1) + (2 * index2) <= 80 Then
                    intarea = index1 * index2
                    intper = (2 * index1) + (2 * index2)
                    putintab(intarea, intper, _
                    inttabarea, intloop1, intloop2, intmax)
                    putintab(intper, intarea, _
                    inttabper, intloop1, intloop2, intmax)
                End If
            Next
        Next
        intloop2 = intmax
    End Sub

    Sub putintab(ByRef intqty1, ByRef intqty2, _
    ByRef inttab, ByRef intloop1, ByRef intloop2, ByRef intmax)
        For index1 As Integer = 0 To intloop1
            If inttab(index1, 0) = 0 Then
                inttab(index1, 0) = intqty1
                inttab(index1, 1) = intqty2
                If 1 > intmax Then
                    intmax = 1
                End If
                Exit Sub
            End If
            If inttab(index1, 0) = intqty1 Then
                For index2 As Integer = 1 To intloop2
                    If inttab(index1, index2) = 0 Then
                        inttab(index1, index2) = intqty2
                        If index2 > intmax Then
                            intmax = intqty2
                        End If
                        Exit Sub
                    End If
                    If inttab(index1, index2) = intqty2 Then
                        Exit Sub
                    End If
                Next
            End If
        Next
    End Sub

    Sub write_answers( _
    ByRef inttabarea, ByRef inttabper, ByRef intloop1, ByRef intloop2)
        Dim strstring As String
        Dim intcount As Integer = 0
        Dim objStreamWriter As StreamWriter
        Console.WriteLine("Writing anser dataset")
        objStreamWriter = _
        New StreamWriter("C:\VB.RECTANGULAR.LOGIC")
        objStreamWriter.WriteLine(strstring)
        For index1 As Integer = 0 To intloop1
            If inttabarea(index1, 0) <> 0 Then
                strstring = "area: " & inttabarea(index1, 0) & _
                " (perimeters: "
                For index2 As Integer = 1 To intloop2
                    If inttabarea(index1, index2) <> 0 Then
                        strstring &= Str(inttabarea(index1, index2))
                    End If
                Next
                strstring &= ")"
                objStreamWriter.WriteLine(strstring)
                intcount += 1
            End If
        Next
        For index1 As Integer = 0 To intloop1
            If inttabper(index1, 0) <> 0 Then
                strstring = "perimeter: " & inttabper(index1, 0) & _
                " (areas: "
                For index2 As Integer = 1 To intloop2
                    If inttabper(index1, index2) <> 0 Then
                        strstring &= Str(inttabper(index1, index2))
                    End If
                Next
                strstring &= ")"
                objStreamWriter.WriteLine(strstring)
                intcount += 1
            End If
        Next
        objStreamWriter.Close()
        Console.WriteLine(intcount & " records written")
    End Sub
End Module

 

 

Edited on February 2, 2005, 11:38 am

Posted by Penny on 2005-02-01 16:23:24