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There was a marathon thread in this subforum that died a long time ago, so I am going to try to start a new one for people to post, solve, and discuss undergraduate mathematics problems. (Of course things like the stackexchange already exist that are fantastic for this purpose, but it would be...

How many distinct bracelets can you make out of a string and n_k beads of colour k for k=1,2,...,m?

Suppose we have an infinite collection of identical planks of wood (which are rectangular prisms that are long in one dimension but short in the other two). We place the first one on a table so that one of its ends is flush with the edge of the table. Place the second one on top of it with all...