MathDB

Form

10A

has

29

students who are listed in order on its duty roster. Form

10B

has

32

students who are listed in order on its duty roster. Every day two students are on duty, one from form

10A

and one from form

10B

. Each day just one of the students on duty changes and is replaced by the following student on the relevant roster (when the last student on a roster is replaced he is replaced by the first). On two particular days the same two students were on duty. Is it possible that starting on the first of these days and ending the day before the second, every pair of students (one from

10A

and one from

10B

) shared duty exactly once?

Problem Statement