Increase cell value with one on worksheet activate

Hello everyone
I have two sheets .. Sheets("INF") and Sheets("List")
I need to put a code in worksheet activate event in List sheet ...every time I activate the List sheet ,range("E1") would increase by one till specific number (according to criteria)

The criteria would be the value of range("B8") in Sheets("INF")
If sheets("INF").range("B8")="Pre" then >> when activating sheets("List") ,range("E1") would be 1 for the first visit ..if I activate another sheet then activate Sheets("List") the range ("E1") would be increased again by one so the new value would be 2 .. then again if I deacativate the List sheet and activate it again the value of range ("E1") would be 3 and this is the end point ...if activated List sheet again the value would be 1 again ..

In other words >>my target is to increase sheets("List").range("E1")
If sheets("INF").range("B8")="Pre" so the changes would be between 1 to 3 only
If sheets("INF").range("B8")="Pri" so the changes would be between 1 to 6 only
Hope it is clear

Great great
Very nice and easy
Can I change my request a little?
I need to change the range("E1") value every 5 seconds in the same way (as another approach)
this action would be in worksheet activate event and when deactivating the sheet the timer stops ...
After activating again the values start over again beginning with the value 1
Thank you very much

Thanks a lot anyway ...you have helped me a lot
Waiting for solutions from experts

Try the attached. This isn't something I do often, but I just helped someone with it the other day. This seems to work, don't know if it's a best-practice way to get it done.

In the List WORKSHEET code module put this.

Option Explicit

Private Sub WORKSHEET_ACTIVATE()
    Me.Range("E1").Value = startVal
    Application.Run "onActivate"
End Sub

Private Sub WORKSHEET_DEACTIVATE()
   On Error Resume Next
   Application.Run "onDeactivate"
End Sub

In a separate (non-object) code module put this:
(Also I gave the "List" worksheet a VBA project 'codeName' of W_LIST)

Option Explicit
Public RunWhen As Double
Public Const startVal = 1
Public Const inc = 1
Public Const howOften = 5
Public Const runWhat = "Active_Process"


Sub scheduleMe(ByVal mySub As String)
    RunWhen = Now + TimeSerial(0, 0, howOften)
    Application.OnTime EarliestTime:=RunWhen, Procedure:=runWhat, schedule:=True
End Sub

Sub Active_Process()
    W_LIST.Range("E1").Value = W_LIST.Range("E1").Value + inc
    Call scheduleMe(runWhat)
End Sub

Private Sub onActivate()
    W_LIST.Range("E1").Value = startVal
    Call scheduleMe(runWhat)
End Sub

Private Sub onDeactivate()
   On Error Resume Next
   Application.OnTime EarliestTime:=RunWhen, Procedure:=runWhat, schedule:=False
End Sub

Great and wonderful ..
Just I need to put an end point as I tested it and noticed it is increased all the time ..
As for "Pre" I need to start at 1 and end at 3
As for "Pri" I need to start at 1 and end at 6
Thanks a lot for help

As for "Pre" I need to start at 1 and end at 3
As for "Pri" I need to start at 1 and end at 6

Ok - I thought you had changed your requirements.

I haven't changed it

In other words >>my target is to increase sheets("List").range("E1")
If sheets("INF").range("B8")="Pre" so the changes would be between 1 to 3 only
If sheets("INF").range("B8")="Pri" so the changes would be between 1 to 6 only

As for "Pre" I need to start at 1 and end at 3
As for "Pri" I need to start at 1 and end at 6

Thank you very very much Mr. Karedog
It works like charm ..
Regards