# Grouping large groups into smaller groups while keeping people together

Let's say we have a grouping of people as such:

   Group People
1      1     40
2      2     40
3      3     43
4      4     15
5      5     41
6      6     10
7      7     23
8      8     17
9      9     32
10    10     31
11    11     21
12    12     12
13    13     25


There are 350 people and the goal of this problem is to group those people into "tables" of size 9.

Rules:

-Make sure that all people are sitting with at least one other person of their original group

-It is best to have 9 people from the same group at the same table but obviously that will not be possible after dividing groups enough times.

-If one person cannot be grouped with another person of their original group, that is okay, but only at the end of the tabling.

-There are 350/9 = 38.88889 possible tables, so we round up to 39 possible tables. The 39th table will have less than 9 people.

Any ideas for the solution of this problem?

Here's a solution where your first rule is prioritized over your second rule:

For each group, the column "Group tables" has the number of tables exclusively occupied by that group, "Leftovers" has the number of people from that group which are not at a group table, and the column "Tables with leftovers" gives the distribution of the leftovers among the remaining tables.

• Thank you for answering! This is a great solution. I am also interested in how you solved other than doing a "sudoku-like" solution? Any way to generalize this solution? – user111417 Aug 7 '17 at 20:59
• I just used some general principles and a little tinkering. E.g. "If a leftover is 1, add a group table to the leftover", "If a leftover is 8 or higher, break up the leftover into smaller pieces", "Leftovers less than 4 cannot be broken up", etc. I don't immediately see a general solution method other than using such principles and brute force. – Jens Aug 7 '17 at 22:36
• Thank you! I hope to find a more general solution, but I like the brute force that's involved sometimes, too. – user111417 Aug 8 '17 at 20:09