The brute force method using VBA for solving an equation with nine unknown variables

Question

This equation: a+(13*b/c)+d+(12*e)-f+(g*h/i)=87 appears when trying to solve the maths puzzle for Vietnamese eight-year-olds that recently became viral all over

Answer 1

I was going to submit another answer but since my last answer was pretty off base I've just overwritten it. This still uses a Monte Carlo style random number approach but it gets a bit lumpy when you have to make sure you haven't already solved with that random number combination.

Sub MonteCarlo()

Dim startTime As Single
startTime = Timer

Dim trialSol As Double
Dim solCounter As Integer
solCounter = 0

Dim trialNums() As Integer

Dim solutions As Collection
Set solutions = New Collection

Dim existingSol As Boolean
existingSol = False

Do

    trialNums = CreateRandomArray

    trialSol = ToSolve(trialNums(1), trialNums(2), _
                       trialNums(3), trialNums(4), _
                       trialNums(5), trialNums(6), _
                       trialNums(7), trialNums(8), _
                       trialNums(9))

    If trialSol = 87 Then

        If Not ExistsIn(solutions, trialNums) Then
            solutions.Add (trialNums)
        End If

    End If

Loop Until (solutions.Count = 128)

Dim solutionTime As Single
solutionTime = Round(Timer - startTime, 5)

Dim i As Integer
For i = 1 To solutions.Count
    Debug.Print "Solution " & i & ":"; vbTab; _
                solutions.Item(i)(1); vbTab; _
                solutions.Item(i)(2); vbTab; _
                solutions.Item(i)(3); vbTab; _
                solutions.Item(i)(4); vbTab; _
                solutions.Item(i)(5); vbTab; _
                solutions.Item(i)(6); vbTab; _
                solutions.Item(i)(7); vbTab; _
                solutions.Item(i)(8); vbTab; _
                solutions.Item(i)(9)
Next i
Debug.Print "Solution time: " & solutionTime & " ms"

End Sub

Function ExistsIn(col As Collection, arr() As Integer) As Boolean

    Dim ei As Boolean
    ei = False
    Dim i As Integer
    Dim temparr() As Integer

    If col.Count > 0 Then
        For i = 1 To col.Count
            temparr = col.Item(i)
            ei = AreEqual(temparr, arr)
        Next i
    End If

    ExistsIn = ei

End Function


Function AreEqual(array1() As Integer, array2() As Integer) As Boolean

    Dim eq As Boolean
    eq = True

    For i = LBound(array1) To UBound(array1)
       If array1(i) <> array2(i) Then
          eq = False
          Exit For
       End If
    Next i

    AreEqual = eq

End Function

Function ToSolve(a As Integer, b As Integer, _
                 c As Integer, d As Integer, _
                 e As Integer, f As Integer, _
                 g As Integer, h As Integer, _
                 i As Integer) As Double

    ToSolve = a + (13 * b / c) + d + (12 * e) - f + (g * h / i)

End Function

Function CreateRandomArray() As Integer()

    Dim numbers As New Collection
    Dim i As Integer

    For i = 1 To 9
        numbers.Add i
    Next i

    Dim rndNums(9) As Integer
    Dim rndInd As Integer

    For i = 1 To 9
        rndInt = CInt(((numbers.Count - 1) * Rnd) + 1)
        rndNums(i) = numbers(rndInt)
        numbers.Remove (rndInt)
    Next i

    CreateRandomArray = rndNums

End Function

My solution time for all combinations is around 3s - 3.5s.