Number Problem

Sean Stevens · Nov 12, 2004

Has anyone come across a solution to this problem.

I have 6 numbers ranging from 1 to 100 in cells A1:A6.

I have a target number in cell C1. Using any combination of the 6 numbers and any combination of the arithemtic signs +,-,* or /, can you reach the target number??

I have been able to do this with just using the + sign, but it gets difficult after that...

Any ideas??? Thanks, Sean.

Sean Stevens · Nov 16, 2004

yee388 - How does the program exit out of the

Do

Loop

if it can't find a combination to get to the target number?? I am using the numbers 75,25,4,8,1,7 and target number of 405. The program has been running for over 30 mins and from stopping and debugging the code, it looks like it is continually looping...

Removed the Do...Loop and it took about 16 minutes to find no combination.

Sean.

Sean Stevens · Nov 16, 2004

Actually looking at those numbers it should have found a solution as

(75-25)*8+4+1 = 405

I guess Excel is evalutaing the calculation as 75-(25*8)+4+1 = -120.

yee388 · Nov 16, 2004

Good call. It's not needed. It was there for a previous version that used it, and I forgot to take it out.

[edit] Just noticed your last post... Yes. I think it would REALLY be difficult to test for all the possible locatations for parentheses....

1+2*3-4
(1+2)*3-4
(1+2*3)-4
(1+2)*(3-4)
1+(2*3)-4

It would take hours...

mdusoe · Nov 16, 2004

You know, I hate these things... I never get any "real" work done

yee, you don't mind if I play, too, do you?

Instead of using Match and CountIf to determine duplicates, I tried using a collection. I keep a collection of every tried formula, and use the formula itself as the item and also as the key. So, every time I try to add to it, and can evaluate Err.Number to determine if it was already used, and that becomes be check for duplicates. This eliminates the need to write anything to the spreadsheet at all.

Here is what I have:

Code:

Sub CountDown()

Dim TriedFormulas As New Collection

Dim ValueArray(8)
Dim OperatorArray(3)
Dim r, c As Long

Application.ScreenUpdating = False

'Get Values from A2:A7
For a = 0 To 5
    ValueArray(a) = Range("A" & a + 2)
Next a

'Initialize operators
OperatorArray(0) = "+"
OperatorArray(1) = "-"
OperatorArray(2) = "/"
OperatorArray(3) = "*"

'Initialize TriedFormulas
For Each temp In TriedFormulas
    TriedFormulas.Remove temp.Index
Next

StartTime = Timer

Do

'Run possibilities for 3 value strings

For i = 0 To 5
For j = 0 To 5
For k = 0 To 5

    For v = 0 To 3
    For w = 0 To 3
    
        txtFormula = ValueArray(i) & OperatorArray(v) & _
                     ValueArray(j) & OperatorArray(w) & ValueArray(k)
        'Make sure all values are unique
        If AlreadyTried(txtFormula, TriedFormulas) Then GoTo SkipValue3
        If Evaluate(txtFormula) = Range("O5").Value Then GoTo ByeBye
    Next w
    Next v
    
SkipValue3:

Next k
Next j
Next i

'Run possibilities for 4 value strings

For i = 0 To 5
For j = 0 To 5
For k = 0 To 5
For l = 0 To 5

    For v = 0 To 3
    For w = 0 To 3
    For x = 0 To 3
    
        txtFormula = ValueArray(i) & OperatorArray(v) & _
                     ValueArray(j) & OperatorArray(w) & _
                     ValueArray(k) & OperatorArray(x) & ValueArray(l)
        
        If AlreadyTried(txtFormula, TriedFormulas) Then GoTo SkipValue4
                     
        If Evaluate(txtFormula) = Range("O5").Value Then GoTo ByeBye
    
    Next x
    Next w
    Next v
    
SkipValue4:

Next l
Next k
Next j
Next i

'Run possibilities for 5 value strings

For i = 0 To 5
For j = 0 To 5
For k = 0 To 5
For l = 0 To 5
For m = 0 To 5

    For v = 0 To 3
    For w = 0 To 3
    For x = 0 To 3
    For y = 0 To 3
    
        txtFormula = ValueArray(i) & OperatorArray(v) & _
                     ValueArray(j) & OperatorArray(w) & _
                     ValueArray(k) & OperatorArray(x) & _
                     ValueArray(l) & OperatorArray(y) & ValueArray(m)
        
        'Make sure all values are unique
        If AlreadyTried(txtFormula, TriedFormulas) Then GoTo SkipValue5
            
        If Evaluate(txtFormula) = Range("O5").Value Then GoTo ByeBye
        
    Next y
    Next x
    Next w
    Next v
    
SkipValue5:

Next m
Next l
Next k
Next j
Next i

'Run possibilities for 6 value strings
For i = 0 To 5
For j = 0 To 5
For k = 0 To 5
For l = 0 To 5
For m = 0 To 5
For n = 0 To 5

    For v = 0 To 3
    For w = 0 To 3
    For x = 0 To 3
    For y = 0 To 3
    For z = 0 To 3
            
        txtFormula = ValueArray(i) & OperatorArray(v) & _
                     ValueArray(j) & OperatorArray(w) & _
                     ValueArray(k) & OperatorArray(x) & _
                     ValueArray(l) & OperatorArray(y) & _
                     ValueArray(m) & OperatorArray(z) & ValueArray(n)
                     
        If AlreadyTried(txtFormula, TriedFormulas) Then GoTo SkipValue6

        If Evaluate(txtFormula) = Range("O5").Value Then GoTo ByeBye
        
    Next z
    Next y
    Next x
    Next w
    Next v
    
SkipValue6:

Next n
Next m
Next l
Next k
Next j
Next i

Loop

MsgBox "Sorry, that goal is not possible."
Exit Sub

ByeBye:

EndTime = Timer

Application.ScreenUpdating = True

MsgBox "Process took " & EndTime - StartTime & " seconds"
MsgBox txtFormula
End Sub

Function AlreadyTried(txtData, colTried As Collection) As Boolean
On Error Resume Next
    colTried.Add txtData, txtData
    AlreadyTried = (Err.Number = 457)
On Error GoTo 0
End Function

Still trying to work out how to incorprate parentheses. But that's after lunch

Mike.

yee388 · Nov 16, 2004

I think the collection idea is great, but I'm not sure we're checking for the same thing.

Say the list of values is 3,3,5,8,50,100

The first formula it will try is 3+3+3, because ValueArray(0) is 3. I want to skip that formula b/c 3 happens 3 times; when it should only be allowed twice.

Maybe I'm misunderstanding your solution...

mdusoe · Nov 16, 2004

Ah, I misunderstood what you were checking for...

Using your example numbers, in the for loops that are:

Code:

For i = 0 To 5 
For j = 0 To 5 
For k = 0 To 5

i=1, j=2,k=3 (or 3+3+5)is exactly the same as i=2, j=1, k=3 (3+3+5). That is what I am checking for. Duplicate combinations of the value arguments.

To cover your check, maybe just verify that all of the subscripts are different. in other words i<>j<>k<>l<>m etc.

Probably a separate function to call.

Hmmm...
Mike.

yee388 · Nov 17, 2004

VerIII:

Can usually find a solution in under 10 secs... if no exact solution can be found, process is under 1 min.

Sub CountDown()

Dim TestArray()
Dim MaxArray(0 To 5, 0 To 5)
Dim ValArray(5)
Dim OpArray(3)
Dim r, c As Long

Range("C9:O9").ClearContents

Application.ScreenUpdating = False

'Get Values from A2:A7
For a = 0 To 5
 ValArray(a) = Range("A" & a + 2)
Next a

'Initialize operators
OpArray(0) = "+"
OpArray(1) = "-"
OpArray(2) = "/"
OpArray(3) = "*"

'Initialize row and column values
r = 1
c = 3

StartTime = Timer

'Run possibilities for 3 value strings

For i = 0 To 5
For j = 0 To 5
For k = 0 To 5

 For v = 0 To 3
 For w = 0 To 3

 'Make sure all values are unique
 If i = j Or i = k Or j = k Then GoTo SkipValue3

 'Test for goal & "closest"
 If Evaluate(ValArray(i) & OpArray(v) & ValArray(j) & OpArray(w) & ValArray(k)) = Range("Goal").Value Then

 'Paste Values
 Cells(9, 3) = ValArray(i)
 Cells(9, 5) = ValArray(j)
 Cells(9, 7) = ValArray(k)
 Cells(9, 4) = OpArray(v)
 Cells(9, 6) = OpArray(w)

 'Paste formula
 Cells(9, 15) = "=" & ValArray(i) & OpArray(v) & ValArray(j) & OpArray(w) & ValArray(k)
 GoTo ByeBye
 End If

 Next w
 Next v

SkipValue3:

Next k
Next j
Next i

'Run possibilities for 4 value strings

For i = 0 To 5
For j = 0 To 5
For k = 0 To 5
For l = 0 To 5

 For v = 0 To 3
 For w = 0 To 3
 For x = 0 To 3

 'Make sure values are unique
 If i = j Or i = k Or i = l Or j = k Or j = l Or k = l Then GoTo SkipValue4

 'Test for goal
 If Evaluate(ValArray(i) & OpArray(v) & ValArray(j) & OpArray(w) & ValArray(k) _
 & OpArray(x) & ValArray(l)) = Range("Goal").Value Then

 'Paste Values
 Cells(9, 3) = ValArray(i)
 Cells(9, 5) = ValArray(j)
 Cells(9, 7) = ValArray(k)
 Cells(9, 9) = ValArray(l)
 Cells(9, 4) = OpArray(v)
 Cells(9, 6) = OpArray(w)
 Cells(9, 8) = OpArray(x)

 'Paste formula
 Cells(9, 15) = "=" & ValArray(i) & OpArray(v) & ValArray(j) & OpArray(w) & ValArray(k) & OpArray(x) & ValArray(l)
 GoTo ByeBye

 End If

 Next x
 Next w
 Next v

SkipValue4:

Next l
Next k
Next j
Next i

'Run possibilities for 5 value strings

For i = 0 To 5
For j = 0 To 5
For k = 0 To 5
For l = 0 To 5
For m = 0 To 5

 For v = 0 To 3
 For w = 0 To 3
 For x = 0 To 3
 For y = 0 To 3

 'Make sure all values are unique
 If i = j Or i = k Or i = l Or i = m Or j = k Or j = l _
 Or j = m Or k = l Or k = m Or l = m Then GoTo SkipValue5

 'Test for goal
 If Evaluate(ValArray(i) & OpArray(v) & ValArray(j) & OpArray(w) & ValArray(k) _
 & OpArray(x) & ValArray(l) & OpArray

& ValArray(m)) = Range("Goal").Value Then

 'Paste Values
 Cells(9, 3) = ValArray(i)
 Cells(9, 5) = ValArray(j)
 Cells(9, 7) = ValArray(k)
 Cells(9, 9) = ValArray(l)
 Cells(9, 11) = ValArray(m)
 Cells(9, 4) = OpArray(v)
 Cells(9, 6) = OpArray(w)
 Cells(9, 8) = OpArray(x)
 Cells(9, 10) = OpArray

'Paste formula
 Cells(9, 15) = "=" & ValArray(i) & OpArray(v) & ValArray(j) & OpArray(w) & ValArray(k) _
 & OpArray(x) & ValArray(l) & OpArray

& ValArray(m)
 GoTo ByeBye

 End If

 Next y
 Next x
 Next w
 Next v

SkipValue5:

Next m
Next l
Next k
Next j
Next i

'Run possibilities for 6 value strings
For i = 0 To 5
For j = 0 To 5
For k = 0 To 5
For l = 0 To 5
For m = 0 To 5
For n = 0 To 5

 For v = 0 To 3
 For w = 0 To 3
 For x = 0 To 3
 For y = 0 To 3
 For z = 0 To 3

 'Make sure all values are unique
 If i = j Or i = k Or i = l Or i = m Or i = n Or j = k Or j = l Or j = m _
 Or j = n Or k = l Or k = m Or k = n Or l = m Or l = n Or m = n Then GoTo SkipValue6

 'Test for goal
 If Evaluate(ValArray(i) & OpArray(v) & ValArray(j) & OpArray(w) & ValArray(k) _
 & OpArray(x) & ValArray(l) & OpArray

& ValArray(m) & OpArray(z) & ValArray

) = Range("Goal").Value Then

 'Paste Values
 Cells(9, 3) = ValArray(i)
 Cells(9, 5) = ValArray(j)
 Cells(9, 7) = ValArray(k)
 Cells(9, 9) = ValArray(l)
 Cells(9, 11) = ValArray(m)
 Cells(9, 13) = ValArray

            Cells(9, 4) = OpArray(v)
            Cells(9, 6) = OpArray(w)
            Cells(9, 8) = OpArray(x)
            Cells(9, 10) = OpArray

Cells(9, 12) = OpArray(z)

 'Paste formula
 Cells(9, 15) = "=" & ValArray(i) & OpArray(v) & ValArray(j) & OpArray(w) & ValArray(k) _
 & OpArray(x) & ValArray(l) & OpArray

& ValArray(m) & OpArray(z) & ValArray

GoTo ByeBye

 End If

 Next z
 Next y
 Next x
 Next w
 Next v

SkipValue6:

Next n
Next m
Next l
Next k
Next j
Next i

MsgBox "Sorry, that goal is not possible."

ByeBye:

EndTime = Timer

[N9] = "="

Application.ScreenUpdating = True

MsgBox "Process took " & EndTime - StartTime & " seconds"

End Sub

GorD · Nov 19, 2004

How do you work this, where do the numbers go?

yee388 · Nov 19, 2004

A2:A7 have the values. Read through the earlier posts to get the whole story on what we're trying to do...

Number Problem

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