### 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.

1. How many coins are there?
2. What's the difference (in cent) between the largest and smallest face values of the coins in Leo's money bus?
3. What's the total value (in dollar) of Leo's coins?
4. What's the average value (in cent) of Leo's coins?
5. What's the median value (in cent) of Leo's coins?
6. How many dollar amounts can Leo make using one or more of his coins?
7. If he can use no more than one coin of each face value, how many positive dollar amounts can Leo make?
8. To make \$0.36, what's the least number of coins shall Leo pick from his money bus?
9. What's the least number of coins that sum to the same value as the coins in Leo's money bus?
10. How many different combinations of coins can Leo make using the coins in his money bus? (A combination has at least one coin.)
11. How many different sets of coins can sum to the same value as the total value of coins in Leo's money bus?
12. 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?