Unique Combos in 7x7 ?

Reply #6

cottoneyedjoe — Sat, 27 Apr 2019 00:46:55 GMT

I thought about it more and worked out the closed-form solution. If the length of the string is K, and you can fill each position with a number from 1 to N non-decreasing, then the total number of valid strings is

(N + K - 1) choose K

equivalently (N+K-1)! / [ (N-1)! * K! ]

With your example it's N = 7 and K = 7, which works out to 1716 with the formula. No script needed

Reply #5

cottoneyedjoe — Mon, 22 Apr 2019 01:15:47 GMT

No problem

Reply #4

WhatAreTheOdds — Mon, 22 Apr 2019 00:28:09 GMT

Thank you so much, Cottoneyedjoe for going to all that trouble to do so. I really appreciate it. I wasn't exactly sure how to calculate it. 1716 is about twice as much as I was hoping for, but at least now I know to think twice before going in that direction

Reply #3

cottoneyedjoe — Mon, 22 Apr 2019 00:04:36 GMT

Okay. I wrote a little program to enumerate all non-decreasing strings of length seven that use only the digits {1, 2, 3, 4, 5, 6, 7} and there are a total of 1716.

Reply #2

WhatAreTheOdds — Sun, 21 Apr 2019 22:16:27 GMT

Thanks for your help. I guess I should have been more clear about one thing - the numbers can only ascend, not descend. So 1111177 is possible, but 7711111 is not. Yes, there are 49 cells (I'm trying to create groupings for my 6/49 lottery).

Reply #1

cottoneyedjoe — Sun, 21 Apr 2019 21:47:22 GMT

I think what you're asking is how many numbers are there between 1111111 and 7777777 (including 1111111 and 7777777 themselves) that contain only the digits {1, 2, 3, 4, 5, 6, 7} with repetition allowed. The answer is 7x7x7x7x7x7x7 = 823543. It's because each digit position can take one of seven different values, and they are all independent of each other, so you multiply 7 by itself seven times.

(If repeated digits were not allowed, the total number of different combinations would be 7x6x5x4... [ More ]

Unique Combos in 7x7 ?

WhatAreTheOdds — Sun, 21 Apr 2019 21:12:53 GMT

How would I calculate the number of unique combinations in a 7x7 grid? If the grid was 7-wide, and was base-7 (not base-10), how many combos would I have? For example, starting with 1111111, 1111112, 1111113, . . . continuing past 1122333, 1122334, 1122335, . . . and all the way to 7777777. I was thinking that perhaps the formula would be (7x7)+(7x6)+(7x5)+(7x4)+(7x3)+(7x2)+(7x1) (which would equal 196), but I thought I'd better ask first (cause I'm just guessing and I may be W-A-Y off).... [ More ]