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Two-dimensional bin packing turns out to be quite a pickle.
I was introduced to the problem as a 13 year old. My Dad’s friend, Keith, noticed I was taking a knack to programming, and wanted to see if I could help him. Keith was (and still is) a carpenter.
Keith wanted me to write a program where he could input a list of shapes, and the program would figure out the best way to cut a board of wood into those shapes, while minimizing scrap wood. Seems reasonable.
My 13 year old mind quickly exploded… I couldn’t figure out one simple, obvious way to do it. Eventually I gave up, to my ego’s dismay (and Keith’s disappointment!).