Socks from a bag

Following instructions she brought home from school, Lillian did her first mathematical induction this evening.

If you put two different pairs of socks in a bag, she figured out that you have to pull out three to be sure that you’ve got a pair – because once you’ve pulled out two, you either have a pair already, or you’ve got one from both pairs, so the next one must match one you’ve already got…

If you put three different pairs of socks in a bag, she figured out that you have to pull out four to be sure that you’ve got a pair… 4 pairs and you need to pull out five…

So you always need to pull out one more than the number of pairs in the bag…

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