The Classroom Seating Problem

I have blogged about the issues of matching students in classes previously. Last night, my son had a task ...

Me: "What are you doing?" 

Son: "The teacher asked me to do the class seating plan." 

Me: "Sounds like fun." 

Son: "No, it isn't fun. I don't know how teachers can do this several times a year. There are four girls who want to be on the same table and three boys. There is one boy who wants to be in a corner. And there are several people who can't be near each other. All that and it has to be boy-girl, boy-girl. It can't be done." 

Me: "Well, you know +Al Roth  won a Nobel prize for doing this with thousands of people. Some of them married." 

Son: "This is harder." 

Me: "That doesn't seem ..." 

Son: "Did he know any of these people? Did he have to turn up to class with them each day if he got it wrong?" 

Me: "I guess not." 

Son: "Maybe he should visit Middle school and deal with really hard problems."

He must have spent 2-3 hours on the problem. Eventually, he decided that the only solution involved re-arranging the design of the classroom to a 'horseshoe' format. It also transpired that the teacher had made the problem even harder as he was required to take into account who would work well together and who might be disruptive together. So it just wasn't about student preferences at all. 

This morning he went to school quite anxious. Having submitted his proposal last night, he had received about 13 lobbying emails from his classmates. I don't think economics is going to invent any algorithms to re-solve all of that any time soon.