Question

Can somebody explain why this doesn’t work? (meaning the variable colorChange stays the same throughout function)

Each array (leftRing and rightRing have integer values of numbers ranging from 1 through 4)

    Private Sub Solve_Click(sender As System.Object, e As System.EventArgs) Handles Solve.Click

    countColorChangesInRings(colorChanges)
    RotateLeftRingClockwise()
    countColorChangesInRings(colorChanges)

    End Sub

    Sub countColorChangesInRings(ByRef var As Integer)

    Dim colorChangesLeft As Integer = 0
    Dim colorChangesRight As Integer = 0
    Dim totalChanges As Integer = 0
    ' Count Color Changes in Left Ring
    For i = 1 To 20
        If (i = 20) Then
            If (leftRing(i) <> leftRing(1)) Then
                colorChangesLeft += 1
            End If
        Else
            If (leftRing(i) <> leftRing(i + 1)) Then
                colorChangesLeft += 1
            End If
        End If
    Next

    ' Count Color Changes in Right Ring
    For i = 1 To 20
        If (i = 20) Then
            If (rightRing(i) <> rightRing(1)) Then
                colorChangesRight += 1
            End If
        Else
            If (rightRing(i) <> rightRing(i + 1)) Then
                colorChangesRight += 1
            End If
        End If
    Next
    totalChanges = colorChangesLeft + colorChangesRight
    var = totalChanges
End Sub

 Sub RotateLeftRingClockwise()
    Dim temp As Integer = leftRing(1)
    ' Rotates Rings clockwise direction
    For i = 1 To 20
        If (i = 20) Then
            leftRing(i) = temp
        Else
            leftRing(i) = leftRing(i + 1)
        End If
    Next
End Sub

Answer 1

From what I can see, it will stay the same.

You basically have a circular buffer of values (due to your special handle when i = 20) and you count the number of times the value changes from index to index.

That number is not going to change if you simply rotate the values through the circular buffer.

Take for example, the array {1, 2, 2, 2, 3, 4}. There are four transitions there, 1-2, 2-3, 3-4 and 4-1.

If you then rotate the list clockwise, you get {4, 1, 2, 2, 2, 3} and the transitions are 4-1, 1-2, 2-3 and 3-4.

In other words, the order of the transitions may change, but the quantity does not.

---

Based on your addition of the RotateLeftRingClockwise code, this is where your problem lies.

Because it simply rotates the left ring, you’re not handling the intersection points of the Hungarian rings correctly. Rotating the left ring would, as well as moving the values around the left ring, change two of the array elements in the right ring (and vice versa), as per the diagram below:

   array element 1 (in a 32-element array)
          |
      +---+---+
      |       |
      V       V
     LLL     RRR
   LL   LL RR   RR
  L       *       R      <- shared cell is left(29)/right(5)
 L       R L       R
 L       R L       R
L       R   L       R
L       R   L       R
L       R   L       R
 L       R L       R
 L       R L       R
  L       *       R      <- shared cell is left(21)/right(13)
   LL   LL RR   RR
 \   LLL     RRR   /
  \               /
   \----->>>-----/
     Direction of
       increasing
         array index

Because your rotate code does not do this, the transition count of both rings will remain identical and hence the sum of them will not change.

For example, say the top-middle cells are array element 1 (as shown) and it increases in a anti-clockwise direction (as your code seems to indicate from the fact that a clockwise rotation shifts from ring[i+1] to ring[i]).

What your code needs to do is first rotate the left ring and then force the new values for the * cells into the right ring, something like:

Sub RotateLeftRingClockwise()
    Dim temp As Integer = leftRing(1)
    For i = 1 To 19
        leftRing(i) = leftRing(i + 1)
    Next
    leftRing(20) = temp

    rightRing( 5) = leftRing(29)
    rightRing(13) = leftRing(21)
End Sub

Those array indexes in the last two lines are specific to my diagram above (32 cells rather than 20), you’ll need to adjust them for your own puzzle.

If you make those changes (and similar ones to your other three rotation functions), you should find that the function starts returning different values. Specifically, rotating the left ring will leave the left value unchanged but should change the right value as different balls come into the intersection point.