Dim Shared As Integer minPasos       'minimal number of steps to get to 1
Dim Shared As Integer Subtractor     '1 or 2
Dim Shared As Integer Ns(20000), Ops(20000), MinNs(20000), MinOps(20000)

Sub Reduce(N As Integer, Paso As Integer) 'Reduce N to 1, recording minimum steps
    If N = 1 Then
        If Paso < minPasos Then
            For i As Integer = 0 To Paso-1
                MinOps(i) = Ops(i)
                MinNs(i) = Ns(i)
            Next i
            minPasos = Paso
        End If
    End If
    If Paso >= minPasos Then Exit Sub     'don't search further
    If N Mod 3 = 0 Then Ops(Paso) = 3 : Ns(Paso) = N/3 : Reduce(N/3, Paso+1)
    If N Mod 2 = 0 Then Ops(Paso) = 2 : Ns(Paso) = N/2 : Reduce(N/2, Paso+1)
    Ops(Paso) = -Subtractor
    Ns(Paso) = N-Subtractor
    Reduce(N-Subtractor, Paso+1)
End Sub

Sub ShowSteps(N As Integer)     'Show minimal steps and how N steps to 1
    minPasos = 50000
    Reduce(N, 0)
    Print "N = " & N & " takes " & minPasos & " steps: N";
    For i As Integer = 0 To minPasos-1
        Print Iif(Sgn(MinOps(i)) < 0, " -", " /");
        Print Abs(MinOps(i)) & "=>" & MinNs(i); '" "
    Next i
    Print
End Sub

Sub ShowCount(Range As Integer) 'Show count of maximum minimal steps and their Ns
    Dim As Integer N, MaxSteps
    MaxSteps = 0          'find maximum number of minimum steps
    For N = 1 To Range
        minPasos = 50000
        Reduce(N, 0)
        If minPasos > MaxSteps Then MaxSteps = minPasos
    Next N
    Print "Maximum steps:"; MaxSteps; " for N =";
    For N = 1 To Range    'show numbers (Ns) for Maximum steps
        minPasos = 50000
        Reduce(N, 0)
        If minPasos = MaxSteps Then Print N; '" ";
    Next N
    Print
End Sub

Dim As Integer N
Subtractor = 1        '1.
For N = 1 To 10
    ShowSteps(N)
Next N
ShowCount(2000)       '2.
ShowCount(20000)      '2a.

Print
Subtractor = 2        '3.
For N = 1 To 10
    ShowSteps(N)
Next N
ShowCount(2000)       '4.
ShowCount(20000)      '4a.
Sleep