|Spoiler Inside: Solution to Puzzle||SelectShow>|
Sometimes, the best way of solving a problem is by not starting at the beginning. Consider #2 first.
Select four socks. You might have a matching pair, but they could all be different. If the first four are all different, the fifth sock must match one of the first four. The answer to #2 is five.
The answer to #1 is three. It does not matter that you have to select the socks in pairs. The selection is still random. To get five socks, you must select three pairs.
The answer to #3 is seven. You will have a pair after five. Remove the pair. Now, you are at three socks, and the situation is just like partway through #2.