I have $25$ people who will be split into groups of $5$ people each day over $5$ days in $5$ different locations. Can I rotate them so that they all meet each other only once and visit each location only once over the $5$ days?
2026-03-25 22:09:17.1774476557
combinations of 5 groups question
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Suppose the groups on day $1$ are $A,B,C,D,E$ visiting venues $1,2,3,4,5$ respectively
Consider the venues visited by the members of group $A$ on day $2$. They've all visited venue $1$ already, so there are five people visiting four venues. Two of them must visit the same venue on day $2$ if they are not to repeat venues. And that contradicts the conditions in the problem.