You may also want to visit some other constraints and "pathalogical cases". e.g. Is it important that sections have the approximately the same size? If so, is giving a student his or her first choice more or less important than keeping sizes similar? What if everyone prefers section 1 as a first choice, 2 as a second, etc? Is the aforementioned lottery "fair" or, as is noted below, are there other criteria applied to give particular students' choices greater weight?

Just some thoughts to get you started tinking...

In reply to Re^2: [OT] simple algorithm for assigning students to class sections by traveler
in thread [OT] simple algorithm for assigning students to class sections by hossman

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