Puzzle 1: You own 9 socks, 3 of which are red and 6 of which are green. You reach into the drawer and grab a number of socks. What is the minimum number of socks you must take in order to guarantee that you have at least one pair of a matching color?
Puzzle 2: You own 1 red sock, 2 indigo socks, 3 blue socks, 4 green socks, 5 yellow socks, 6 orange socks, and 7 violet socks. How many socks must you grab from your drawer in order to guarantee at least one pair of a matching color?
Puzzle 3: You own 25 socks, some of which are red; the rest are indigo. If you reach into the drawer and pick two socks, the chances are exactly even that you will have a matching pair. If you have more red socks than indigo socks, how many do you have of each color?
Puzzle 4: Continuing from problem 3, we now assume that someone gives you a certain number of blue socks to add to your collection of red and indigo. Amazingly enough, it is still true that if you reach into the drawer and pick two, you get a match with even odds. How many blue socks did you receive?
I give up, show me the solution.