Suppose you break your piggy bank and scoop up a handful of 22 coins (pennies, nickels, dimes and quarters). Prove that you must have at least 6 coins of a single denomination. Suppose you have an odd number of pennies. Prove that you must have an odd number of at least one of the other types of coins. How many coins would you scoop up to be sure that you either had 4 coins that were all the same or 4 coins that were all different. Prove your answer.