Dad proposed a problem for Midnight Math tonight that went something like this: I have two colors of socks in my drawers and I want to wear matching socks, but I don't want to take extra time trying to find matches. I want to reach into my drawer, without looking, and pull out enough socks to guarantee I have a matched pair, but no more. What is the fewest number of socks I need to pull out to be certain I will get a match?
They discussed this at length, with Nigel going from two socks to four socks as his guess right at the beginning. After some discussion he settled on three as being his answer. They continued to talk about why that was for a few more minutes.
The next night, Dad asked what would happen if he had three legs and wanted to get a matching triplet of socks. After determining it would take five socks to guarantee a match, Dad started diagramming out the answers they had discovered so far. Nigel saw that it would take seven socks to get a matching quadruple before Dad got to writing that part of the chart, and stumbled a bit on adding twos to the odd numbers (wanting to switch to counting even numbers by twos), but was able to see the trend quite easily.
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