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Timetabling choreography with maths

Earlier this week my sister-in-law (“SIL” from now on) sent me an email asking for help. She’s a dance teacher, and her class need to rehearse their group pieces before their exam. She’d been trying to work out how to timetable the groups’ rehearsals, and couldn’t make it all fit together. So of course, she asked her friendly neighbourhood mathmo for help.

My initial reply was cheery and optimistic. It’s always good to let people think you know what you’re doing: much like one of Evel Knievel’s stunts, it makes you look even better on the occasions you succeed.

I’d half-remembered Katie’s friend’s Dad’s golf tournament problem and made a guess about the root of the difficulty she was having, but on closer inspection it wasn’t quite the same. I’m going to try to recount the process of coming up with an answer as it happened, with wrong turns and half-baked ideas included.