# Combinatorics question

• B
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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?