I have a math problem I need help with for my work, any help would be greatly appreciated! Never mind the specifics, here are the parameters:
10 rows or less
46 colums (or less)
Alternate rows MUST have one less (e.g. 46, 45, 46, 45…)
All these groups must fit into the 46 by 10 space:
1 group of 15
5 groups of 14
9 groups of 13
8 groups of 12
3 groups of 11
1 group of 10
1 group of 9
1 group of 5
1 group of 4
Special
1 group of 23 - OR - split into 1 group of 10 and 1 group of 13
And
1 group of 17 - OR - split into 1 group of 10 and 1 group of 7
Groups cannot spill onto other rows except the 2 special groups
Can this be solved? Or will I need to add more columns? I CANNOT add more rows.
I really appreciate any help with this.
Does this satisfy the problem constraints?
15 14 13 4 (46, done with 15s and 4s)
14 13 13 5 (45, done with 5s)
14 13 10 9 (46, done with 9s)
14 11 10 10 (45, done with 10s)
13 13 13 7 (46, done with 7s)
14 13 13 (40, done with 14s)
13 12 12 (37, done with 13s)
12 12 12 (36)
12 12 11 (35)
12 11 11 (34, done with 12s and 11s)
I basically did this using a mostly-greedy algorithm by hand: try to fill with big groups, then shrink the groups slightly to fill the empty spaces using small groups. This made it feasible to have rather small rows at the end after running out of small groups, since you have a rather large margin of empty spaces (~60) in your overall array. But I do not know if the small rows are acceptable. Nor do I know if the fact that I split the special groups over non-adjacent rows in some cases was acceptable.