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We're leaving polyominoes behind in favor of socks!
The idea in these questions is to further introduce and extend the idea of proof. Chances are you've heard some version of the sock problem posed in Q1 and by itself it's just a different exercise in working out conditions for some mathematical object to be inevitable (here, a matching pair of socks). With the remaining questions, however, what I wanted to do is start introducing the idea of pursuing more general questions given a specific starting point. We do this by broadening the conditions that constrain the original scenario: What if the monster has more sock colors? What if the monster has more feet? What if both things are true? Besides solving these problems, thinking about other ways to generalize the question is part of what I'm hoping to get kids to do here.
I'm a little hard-pressed to think of a good supporting resource for this, but I will take the chance to mention Paul Erdos' biography "My Brain is Open." There's a bit in there where the author talks about Erdos' quest for ever more general theorems, which is really what this assignment is trying to introduce (very gently). If you haven't read about Erdos, definitely check out this book.