# Thread: Permutations (A2k)

1. ## Permutations (A2k)

I have a range consisting of 40 cells - 8 rows by 5 columns. Each row consists of 5 digits. I need to display every permutation of one digit taken from each row to form a series of rows each containing eight digits. I hope I've phrased my requirements comprehensibly. Would any kind soul supply some code to achieve this?
TIA.

2. ## Re: Permutations (A2k)

Rob,

Designing a new puzzle <img src=/S/evilgrin.gif border=0 alt=evilgrin width=15 height=15>?

I hope you realise that there are 5 to the power 8 = 390625 possible choices (if the digits in a row are different). You say you want to display them all - that's going to take time! And it exceeds the max number of 65536 rows in a worksheet.

What do you want to achieve?

3. ## Re: Permutations (A2k)

If I understand:

You have 8 rows and 5 cols. each cell of this 8x5 matrix contains 1 number.
You want to take 1 number (out of the 5 columns) from each row and combine them into 1 8-digit number.

You want all the permutations (I calculate 5^8 permutations = 390,625) of this?

Where do you want the results and how do want them displayed. Do you want the list in any sort of Matrix (25 col x 15,625 rows; or 125 col x 3,125 rows) or just fill a column and when it gets full to just go to the next column (and this will take just shy of 6 FULL excel columns to list them.)

Steve

4. ## Re: Permutations (A2k)

Very astute, Hans, but not quite. After a long day, to my shame, I'm trying to take the easy way out and use any such code to help me solve puzzles of a particular type - sort of defeats the object really. I shall rely on my brain to filter out the nonsense combinations and attack the problem anew, tomorrow. Still, a general approach to such problems would be useful for future projects and if you have the time or inclination your thoughts would be valued. But at your leisure: you have more important problems to focus on. <img src=/S/newbrain.gif border=0 alt=newbrain width=21 height=22>

5. ## Re: Permutations (A2k)

Sorry Steve! I had a rush of blood to the foot (where my brain resides).Your post arrived mid-reply to Hans.

6. ## Re: Permutations (A2k)

If there are not 5^8 permutations, what combinations are not used?

What kind of puzzles are you trying to solve? It is sometimes an interesting puzzle to try to figure generic algorithms for solving puzzles.

Steve

7. ## Re: Permutations (A2k)

Steve,

I think that Rob (bandido) was trying to solve the puzzle in <post#=230187>post 230187</post#> in the Puzzles forum by brute force.

8. ## Re: Permutations (A2k)

Hans,
Ok that explains the reason, though I still say there are 5^8 permutations, the way he stated it.

I guess he could mean that he already has the 8 letters (1 from each row) removed (to leave the 8 NEW words) and wants the 8! =40,320 combinations of those 8 letters.

Steve

9. ## Re: Permutations (A2k)

<img src=/S/cop.gif border=0 alt=cop width=15 height=24> I love it! I've got you reaching for permutations...

Since the word BREAD contains many possibilities, I'll tell you that you can grab the A and move on... <img src=/S/evilgrin.gif border=0 alt=evilgrin width=15 height=15>

10. ## Re: Permutations (A2k)

Steve,
I originally wanted to find out how many valid, eight letter English words I could create by taking one letter from each row. However, I solved Ricky's puzzle very quickly by visual inspection.
It was how you would approach this type of problem using Excel, VB or both that intrigued me.

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