How to display the solution to this challenge

[Aussiebear]

This challenge to you is to show a solution to the following question.

"Delroy the cat is taking a snooze, dreaming he is encircled by 13 mice — 12 brown, 1 white. Delroy's owner says he can eat all of the mice except the white one. Delroy must also count in a circle and only eat every 13th mouse. Where should Delroy begin counting to ensure he eats the 12 brown mice? How many times around the circle does Delroy need to count?"

How would you go about calculating an answer?

[jdelano]

Hack code of, white mouse is in position 9 and start counting at position 2


Private Sub CommandButton1_Click()


Dim eatenCount As Integer
Dim mouseCount As Integer
Dim sheetRow As Integer
Dim mouseColor As String
Dim mouseStatus As String

Sheet1.Range("C3:C15").Value = ""
Sheet1.Cells(3, 4).Value = 0

mouseCount = 1
sheetRow = Sheet1.Cells(2, 6).Value
eatenCount = 0

Do While True
mouseColor = Sheet1.Cells(sheetRow, 1).Value
mouseStatus = Sheet1.Cells(sheetRow, 3).Value

' count only the uneaten meece
If mouseStatus = "" Then
If mouseCount = 13 And mouseColor = "Brown" Then
' this is okay to eat
Sheet1.Cells(3, 4).Value = Sheet1.Cells(3, 4).Value + 1
Sheet1.Cells(sheetRow, 3).Value = "Eaten (" & Sheet1.Cells(3, 4).Value & ")"
mouseCount = 0


ElseIf mouseCount = 13 And mouseColor = "White" Then
' can't eat the white one
MsgBox "13th mouse is white"
Exit Sub
End If

sheetRow = sheetRow + 1

mouseCount = mouseCount + 1
Else
' still need to move the row
sheetRow = sheetRow + 1
End If

If sheetRow = 16 Then
sheetRow = Sheet1.Cells(2, 6).Value - 1 ' go back to the top of the list
If sheetRow = 2 Then sheetRow = 3 ' don't start a loop on the headings
End If

If mouseCount = 14 Then Exit Do

Loop

MsgBox "exited loop"

End Sub

[Aussiebear]

Thank you jdelano, that's one version. Anyone else like to have a crack at it?

From the graphic below, I was thinking that with the White Mouse in position 1 and the Brown Mice occupying Positions 2 to 13, and starting the victims at Position 2, all is well until day 11 in which our infamous mouse becomes "Main Course of the Day". Position 10 appears to be the best option for the White Mouse.

How do I prove this with vba?

31898

[Aussiebear]

Okay maybe this will suffice


Sub DelroyMouse()
Dim numMice As Integer
Dim skipCount As Integer
Dim mice() As Boolean
Dim currentPosition As Integer
Dim count As Integer
Dim rounds As Integer
Dim startingPosition As Integer
Dim i As Integer
numMice = 13
skipCount = 13
' Test starting positions from 1 to 13
For startingPosition = 1 To numMice
ReDim mice(1 To numMice)
For i = 1 To numMice
mice(i) = True
' Initialize all mice as edible
Next i
mice(numMice) = False
' Mark the white mouse as inedible
currentPosition = startingPosition
count = 0
rounds = 0
Do While True
count = count + 1
currentPosition = ((currentPosition + skipCount - 2) Mod numMice) + 1 'Adjusted for VBA 1 based arrays.
If mice(currentPosition) Then
mice(currentPosition) = False
If Not HasTrue(mice) Then
' Check if all brown mice are eaten
MsgBox "Delroy should start counting from mouse number " & startingPosition & "." & vbCrLf & _
"Delroy needs to count around the circle " & rounds & " times."
Exit Sub
End If
End If
If currentPosition = 1 Then
rounds = rounds + 1
End If
Loop
Next startingPosition
End Sub

Function HasTrue(arr() As Boolean) As Boolean
Dim i As Integer
For i = LBound(arr) To UBound(arr)
If arr(i) = True Then
HasTrue = True
Exit Function
End If
Next i
HasTrue = False
End Function

[jdelano]

Nice!