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Edited by Richard Walker, Sunday, 29 May 2022, 23:44

9 students and 9 professors attend a dinner at which they sit at a round table. The organisers wish to arrange the seating so that no one is seated between two professors. Is this possible?

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One odd-looking arrangement would be to seat all the professors together and therefore likewise for the students. At both ends of the row of students each of the two students so positioned would have a professor on one side and a student at the other. Ditto, of course for the professors.

I suspect there is another solution or, perhaps more than one more, but I think this is a possible one.

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My answer is based on no student being between two professors. If this is a correct interpretation then an arrangement of three professors three students x3 would, I think, also work.

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If what is meant is that literally no-one, professor or student, is seated between two professors then the combination  AB,AB,AB,AB,AB,AB,AB,AB,AB, where A=professor and B = student, seated in a circle should work. If I imagine this row stretched into a circle then A will meet B and the formation will be sustained.

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Oops!!! My last posting is clearly wrong. A is between Bx2 on nine occasions and vice versa..

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A-= PROFESSOR     B=STUDENT

AB, BA, AB, BA, AB, BA, AB, BA, BA.

If I literally wrap this line into a circle two professors will meet. At no point that I can see will any one student be between two professors.

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AB, BA, AB, BA, AB, BA, AB, BA, BA.

This student is between two profs though.

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AB, BA, AB, BA, AB, BA, AB, BA, BA.

This student is between two profs though.

AB, BA, AB, BA, AB, BA, AB, BA, AB.

Yes you're right of course Richard. So if I rearrange the seating as shown, when B meets A s/he will still be between two professors. The answer appears to be that such an arrangement is not possible. Can't understand how I didn't see that last seating arrangement.

Really interesting problem and if such an arrangement is possible, can't wait to see it.

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AB, BA, AB, BA, AB, BA, AB, BB, AA.

Is this combination allowable?

THERE IS NO ONE STUDENT BETWEEN TWO PROFESSORS THAT I CAN SEE. SAID THAT BEFORE😀