SOLUTION: Ana has one coin of 5 cents, one coin of 10 cents, one coin of 20 cents and one coin of 50 cents. How many possible values she can make from these coins.

No 1 2,3,4, or 5 of those coins add up to the same value
as any other 1,2,3,4, or 5, so every combination of coins
gives a different value.

There are two choices we can make for each coin.
They are:

1. Use it to form a value.
2. Do not use it to form a value.

There are 2 choices to make for the 5 cent coin. (Use it or don't).
There are 2 choices to make for the 10 cent coin.
There are 2 choices to make for the 20 cent coin.
There are 2 choices to make for the 50 cent coin.

Therefore there are 2×2×2×2 = 24 = 16 different values.
However that includes the value 0, in which case we do not use any 
coins.  So we exclude the value 0 from the 16:

Answer = 15 values (not counting 0 cents).

These values are every multiple of 5 cents from 5 cents through 85
cents, EXCEPT there is no way to have 40 cents or 45 cents.

Edwin