High School Generating Teams to Equally Distribute Papers for Evaluating

[kuruman]

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?

 

[mfb]

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.

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