### Coin Problems

Leo has a money bus to collect his savings. After buying his favorite Lego set, Leo has a few coins left, including 4 pennies, 3 nickels, 2 dimes and 1 quarter. For the following problems, we only consider four types of coins: pennies, nickels, dimes and quarters.

- How many coins are there?
- What's the difference (in cent) between the largest and smallest face values of the coins in Leo's money bus?
- What's the total value (in dollar) of Leo's coins?
- What's the average value (in cent) of Leo's coins?
- What's the median value (in cent) of Leo's coins?
- How many dollar amounts can Leo make using one or more of his coins?
- If he can use no more than one coin of each face value, how many positive dollar amounts can Leo make?
- To make $0.36, what's the least number of coins shall Leo pick from his money bus?
- What's the least number of coins that sum to the same value as the coins in Leo's money bus?
- How many different combinations of coins can Leo make using the coins in his money bus? (A combination has at least one coin.)
- How many different sets of coins can sum to the same value as the total value of coins in Leo's money bus?
- If Leo redesigned the face values of coins, what's the least number of face values shall he use to minimize the total number of coins that can cover all values from 1 cent to the total value of the coins in Leo's money bus?