Combinatorics question

  • B
  • Thread starter kuruman
  • Start date
  • #1
kuruman
Science Advisor
Homework Helper
Insights Author
Gold Member
9,553
2,858
I have ##N## papers to be evaluated, ##40 \le N \le 56##. I have 9 people named A - I that need to be put in teams of 3 to evaluate the papers individually, i.e. 3 evaluations per paper. There are ##\begin{pmatrix}9 \\3\end{pmatrix} =84## triplets that can be formed. Thus there are more teams than papers. The constraint in forming the teams is that any member will evaluate at most one more paper than any other member. My approach so far has been to use determinants to form triplets. For example, ##\begin{vmatrix} A & B & C \\ D & E & F \\ G & H &I \end{vmatrix} ## gives 6 triplets with each letter appearing twice. Thus, the equal distribution of load can be achieved if ##N## is a multiple of 6. If it isn't, the remainder can be assigned by hand. There should be 14 such determinants. My question is how do I generate them uniquely?
 

Answers and Replies

  • #2
34,987
11,172
Do the teams need to be different for every paper? If not then the trivial approach is to make three teams, ABC, DEF, GHI, assign 1/3 to each team. Then you get exactly equal load for every multiple of 3, and differences of 1 for every other number, something you cannot avoid in these cases.

As additional benefits it makes scheduling meetings easier and limits the spread of infectious diseases better.
 

Related Threads on Combinatorics question

  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
4
Views
2K
Replies
2
Views
674
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
736
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
14
Views
4K
Top