[2008] List all possible sums of a combination

[[hip,hip]]

I need some help with a math problem I'm trying to work out with visual basic.
I need to calculate the probability of having a certain sum when randomly choosing 5 of 36 possible numbers.
I already know all of the 36 possible numbers, and I know what the total number of possibilities is, I just need to write some code that will list all of the possible sums for me when you add any five of those thirty six numbers together. Ideally I would be able to also have it count how many of a certain sum occurred, but even if I could just have them as a list and I just count the instances, that would be fine too. Any help would be greatly appreciated, even if you could just give me a kick in the right direction.

[Mur16]

Post some of the code you've written so far

[CrashPilot]

This should work (tested it and it did for me)

        Dim myList As New List(Of Integer)      'Contains the list of all numbers
        Dim A As UInteger = 1                   'Some counter variables
        Dim B As UInteger = 1
        Dim C As UInteger = 1
        Dim D As UInteger = 1
        Dim F As UInteger = 1

        While True                              'I break when the last variable (A) reaches > 36
            myList.Add(A + B + C + D + F)       'I just increment F till it gets bigger then 36
            F += 1                              'I then reset it to 1 and increment D with one
            If F > 36 Then                      'this is repeated for all untill finally A gets > 36
                F = 1
                D += 1
            End If
            If D > 36 Then
                D = 1
                C += 1
            End If
            If C > 36 Then
                C = 1
                B += 1
            End If
            If B > 36 Then
                B = 1
                A += 1
            End If
            If A > 36 Then
                Exit While                      '<----Thats here
            End If
        End While

        Dim myHisto(180) As Integer             'An array to create a histogram, cinse
        Array.Clear(myHisto, 0, myHisto.Count)  'The maximum value = 180 (5 X 36) so I create one of 
        For Each entry As Integer In myList     'a length of 181 (Zero indexed!) I do this becouse it 
            myHisto(entry) += 1                 'makes filling easier and the index represents the 
        Next                                    'actual number (so not: 155 = actually the count of 156)

        Dim MaxCount As Integer = 0             'Some vars to store the max value and index of the histogram
        Dim MaxCountIndex As Integer = 0

        For Indexer As Integer = 0 To myHisto.Count - 1 'Loop through the histo printing the values and percentage chance
            'Replace the debug with something usefull. like a datagrid or console.print
            Debug.Print(String.Format("{0}{1}:{2}{3} = {4}&#37;", Indexer.ToString, vbTab, vbTab, myHisto(Indexer).ToString, CSng(myHisto(Indexer) / Math.Pow(36, 5) * 100)))
            If myHisto(Indexer) > MaxCount Then         'This filters the maximum count and 
                MaxCount = myHisto(Indexer)             'stores it in maxCount
                MaxCountIndex = Indexer                 'I also store the index which is the max count value
            End If
        Next

        Debug.Print(MaxCount.ToString & "   |   " & MaxCountIndex.ToString)    'And finally print it all
        'Please note that your example has two maximum thrown values, 92 and 93 I only show 92 here
        'I leave it to you to fix that
    End Sub

Now please note that this is definitly not the prettiest answer but allowing for the KISS tradition
(and just 15 minutes of work) this is the Simplest solution and therefor not prone to bugs and debugging is easy. The code
can be a lot shorter using somthing like recusion.

*Edit*
btw: If you would Add the minimal number thrown to the maximum and devide it by 2 you also get the answer:
Two D6:
Minimum: 2
Maximum: 12
Total = 14
14 / 2 = 7 (wattayouknow?)

So:
Min 5
Max 180
Total 185
185 / 2 = 92.5 (mhhrrrm)
AH! 92 and 93 (round down and up)
This doesn't give you the total list of all thrown thoug :P

(p.s. You got some funky dice :P)

[DataMiser]

That does not look right.

[CrashPilot]

That does not look right.

Looking wrong doesn't make it wrong untill you can deliver a reason why you believe it is wrong. For up to now this is a useless comment unless you are trying to farm posts then it would be usefull to you .

[DataMiser]

Well for one thing I assume that 5 numbers from a possible 36 would mean 5 different numbers where the code posted starts by adding 1+1+1+1+1 does not seem to fit the question from the OP. Of course I could be wrong and that may be what he is looking for just not what I get from it.

[DataMiser]

If I am correct in assuming that you can not pick the same number 5 times then the code needs to be much different.

I am thinking a set of nested for next loops with a > test in each to make sure that each combination of numbers is used only once and the same number does not appear twice in the same equation.

[CrashPilot]

I totally agree, if that were the case. I dont see him stating that each number must be unique just one of the 36 possibilities. I am not saying that I am right or wrong for that matter we'll have to wait for the author to clear that up.

I personally thought this was a classic dice problem, you have 5 dice (D36), which number(s) would have the most chance of being thrown.

I am sorry if you feel like I took a swing at ya, but I dislike answers as "You are wrong" or "I dissagree" and 99% of the time those belong to postfarmers that like shiny titles :S.
(clearly not you)

[[hip,hip]]

You could pick the same number five times, so that code is beautiful! Thanks a lot!

[dglienna]

List all possible sums of a combination

Is a classic Factorial() problem. 5! = 1*2*3*4*5 = 120

So, to resolve it, MARK IT RESOLVED using THREAD TOOLS!