5 digit number combinations

**Puppiie** · 09-02-2010, 10:15 AM

I need all the 5 digit number combination using the character 0-9, but there cannot not be any duplicate numbers.

For example, 01198, 02297, these couldn't be used as they have duplicate numbers.

Once the numbers with duplicate numerals have been removed, I need to come up with a formula that will remove every additional number that contains the same 5 numerals. For example, if I already have 01234, I need to remove (or somehow identify) every other combination of those four numbers....12340, 24301, 30124, etc

**MarvinP** · 09-02-2010, 10:24 AM

Read this first
http://www.mathsisfun.com/combinator...mutations.html

Combinations or Permutations?

**Puppiie** · 09-02-2010, 10:33 AM

It is a combination

**MarvinP** · 09-02-2010, 10:37 AM

Did you read down the page for Combinations without repititions?
Do you want us to list all the numbers for you in cells in Excel?
How many numbers will there be?

**Puppiie** · 09-02-2010, 10:42 AM

If you read my post properly you can tell i asked for it without repititions, yes or just a code so i can do it myself easily.

I have no idea how many numbers its whi im asking.

**MarvinP** · 09-02-2010, 10:53 AM

Hi Puppiie,
I'm not trying to be dumb, but your original post was confusing for me. I'm confused between your use of of the words number and digit.

In your second sentence in your post you said that:
For example, 01198, 02297, these couldn't be used as they have duplicate numbers.

I couldn't tell if the problem(s) with these was that 0 and 9 (digits) had been used in both numbers or if it was because you didn't allow the 1 digit to be used in a single number.

I've taught combinations and permutations in the past and it is always confusing if there are replacements or not and how to structure the problem correctly.

This is why I'm asking.

**Puppiie** · 09-02-2010, 10:55 AM

Oh sorry about the confusion

i didn't mean the mubers 0 and 9 i ment because in each of the 5 digits there 2 ones and in the other 2 twos.

Sorry for the confusion hope this helps

**MarvinP** · 09-02-2010, 11:17 AM

Would the sum of the digits being unique solve your problem?
0+1+2+3+4 = 10 , ...., 5+6+7+8+9 = 35

**Paul** · 09-02-2010, 11:23 AM

Not sure how that would work, Marvin.. as 01567 summed is the same as 20467. (And many other matching sums)

**MarvinP** · 09-02-2010, 11:35 AM

Hi Paul,
The teacher in me is coming out. You are absolutely correct and I knew that.

Now - are there C(10,5) = 252 possible numbers?

Let Puppiie struggle a little bit with that question before we provide an answer.

I'm exploring pulling the digits out of the 5 digit number, sorting them and putting back as a number.

Would this accomplish the task? Example: 43210 -> 01234 as would 34012 -> 01234 after sorting digits.
Then each 5 digit number would have a value and could eliminate dupicates in the question asked.

I've used the sum of the digits before as an easy first test to see if I need to go further in the test.

**Puppiie** · 09-02-2010, 12:40 PM

I'm not going to lie you have got me a bit confused.

but you are right i could not have 43210 aswell as 01234 because the order of the numbers do not matter.

**MarvinP** · 09-02-2010, 02:03 PM

Puppiie -

You confusion is GREAT! As we try to give answers, it's important for us to understand your question. You have to decide if 01234 is the same as 43210. It was not obvious, to me, from your original post.

I decided you wanted to say that 12345 was the same as 54321. I've written a User Defined Function that sorts (from small to large) 5 digits and returns the value. Example 54321 = 12345 , 13245 = 12345 ect.

If you use this function in a column next to your text digits it will be easier to tell which are the same, as the value will be the same.

'This function takes a 5 character long string
'Made up of digits from 0-9 (no repeating digits)
'Returns the minimim value of the 5 digits as a test for uniqueness

Function MinValue5String(NumStr As String) As Double

Dim Ctr As Integer
Dim Ctr2 As Integer
Dim Vals(5) As Integer
Dim SortVals(5) As Integer
Dim MinVal As Double

'Test to see if exactly 5 character long string
If Len(NumStr) <> 5 Then
    MsgBox ("Need 5 characters in the number string")
    GoTo Not5Long
End If

For Ctr = 1 To 5
    Vals(Ctr) = Mid(NumStr, Ctr, 1)
Next Ctr

'Sort the numbers small to large
For Ctr2 = 1 To 4
    For Ctr = 1 To 4
        If Vals(Ctr) > Vals(Ctr + 1) Then
            Vals(0) = Vals(Ctr)
            Vals(Ctr) = Vals(Ctr + 1)
            Vals(Ctr + 1) = Vals(0)
        End If
    Next Ctr
Next Ctr2

'Test to see if any digits repeat
For Ctr = 1 To 4
    If Vals(Ctr) = Vals(Ctr + 1) Then
        MsgBox ("Two digits are the same - not allowed")
        GoTo Not5Long
    End If
Next Ctr

'Build value of digits
MinValue5String = 0
For Ctr = 1 To 5
    MinValue5String = MinValue5String + Vals(Ctr) * 10 ^ (5 - Ctr)
Next Ctr

Not5Long:

End Function

To use the above User Defined Function (UDF)

If A1 contains "43267" (any 5 character string of digits)
In B1 type "=MinValue5String(A1)"
B1 will then show the value 23467.

I'm not sure this answers your entire question but may be a start for determining if any 2 Five Digit strings have the same exact 5 digits in them as another (based on their minimum 5 digit values).

**Puppiie** · 09-02-2010, 03:33 PM

I am sorry but i am a complete fool, is it possible to get a list f numbers i am really struggling with this =/

**shg** · 09-02-2010, 04:19 PM

        --a-- --b-- --c-- --d-- --e-- --f--
    1   43210 53210 63210 73210 83210 93210
    2         54210 64210 74210 84210 94210
    3         54310 64310 74310 84310 94310
    4         54320 64320 74320 84320 94320
    5         54321 64321 74321 84321 94321
    6               65210 75210 85210 95210
    7               65310 75310 85310 95310
    8               65320 75320 85320 95320
    9               65321 75321 85321 95321
   10               65410 75410 85410 95410
   11               65420 75420 85420 95420
   12               65421 75421 85421 95421
   13               65430 75430 85430 95430
   14               65431 75431 85431 95431
   15               65432 75432 85432 95432
   16                     76210 86210 96210
   17                     76310 86310 96310
   18                     76320 86320 96320
   19                     76321 86321 96321
   20                     76410 86410 96410
   21                     76420 86420 96420
   22                     76421 86421 96421
   23                     76430 86430 96430
   24                     76431 86431 96431
   25                     76432 86432 96432
   26                     76510 86510 96510
   27                     76520 86520 96520
   28                     76521 86521 96521
   29                     76530 86530 96530
   30                     76531 86531 96531
   31                     76532 86532 96532
   32                     76540 86540 96540
   33                     76541 86541 96541
   34                     76542 86542 96542
   35                     76543 86543 96543
   36                           87210 97210
   37                           87310 97310
   38                           87320 97320
   39                           87321 97321
   40                           87410 97410
   41                           87420 97420
   42                           87421 97421
   43                           87430 97430
   44                           87431 97431
   45                           87432 97432
   46                           87510 97510
   47                           87520 97520
   48                           87521 97521
   49                           87530 97530
   50                           87531 97531
   51                           87532 97532
   52                           87540 97540
   53                           87541 97541
   54                           87542 97542
   55                           87543 97543
   56                           87610 97610
   57                           87620 97620
   58                           87621 97621
   59                           87630 97630
   60                           87631 97631
   61                           87632 97632
   62                           87640 97640
   63                           87641 97641
   64                           87642 97642
   65                           87643 97643
   66                           87650 97650
   67                           87651 97651
   68                           87652 97652
   69                           87653 97653
   70                           87654 97654
   71                                 98210
   72                                 98310
   73                                 98320
   74                                 98321
   75                                 98410
   76                                 98420
   77                                 98421
   78                                 98430
   79                                 98431
   80                                 98432
   81                                 98510
   82                                 98520
   83                                 98521
   84                                 98530
   85                                 98531
   86                                 98532
   87                                 98540
   88                                 98541
   89                                 98542
   90                                 98543
   91                                 98610
   92                                 98620
   93                                 98621
   94                                 98630
   95                                 98631
   96                                 98632
   97                                 98640
   98                                 98641
   99                                 98642
  100                                 98643
  101                                 98650
  102                                 98651
  103                                 98652
  104                                 98653
  105                                 98654
  106                                 98710
  107                                 98720
  108                                 98721
  109                                 98730
  110                                 98731
  111                                 98732
  112                                 98740
  113                                 98741
  114                                 98742
  115                                 98743
  116                                 98750
  117                                 98751
  118                                 98752
  119                                 98753
  120                                 98754
  121                                 98760
  122                                 98761
  123                                 98762
  124                                 98763
  125                                 98764
  126                                 98765

**Puppiie** · 09-02-2010, 05:02 PM

Thanks SHG you helped me crack my lockbox!!!

5 digit number combinations

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