How many combinations of pennies, dimes, nickels, and quarters create 0.32$? I need help solving this. I cannot find the complete number of combinations. I have already found $5$, but I can't find any more.
 A: First consider quarters.  You could have either no quarters (leaving $32$ cents to be covered by pennies, nickels and dimes) or one quarter (leaving $7$ cents).  Diagram:
     (32) 
  [0 quarters]        [1 quarter]         
     (32)                (7)

Next, consider dimes.  In the first case you could have 0, 1 or 2 dimes, in the second you must have 0.  Diagram:
     (32)
  [0 quarters]                              [1 quarter]         
     (32)                                      (7) 
[0 dimes]    [1 dime]    [2 dimes]          [0 dimes]
  (32)         (22)         (2)                (7)

Next consider nickels.  Finally, everything left over must be done with pennies.
A: Leaving out the pennies in each combo ...
There are 2 combos with a quarter:
25+5 (that is: 1 quarter + 1 nickel ...so 2 pennies...)
25 (So just a quarter ...so 7 pennies ...  for combos below, you'll have to figure out how many pennies to add ...)
There is 1 combo with 3 dimes: 
10+10+10
There are 3 combos with 2 dimes:
10+10+5+5
10+10+5
10+10
There are 5 combos with 1 dime:
10+5+5+5+5
10+5+5+5
10+5+5
10+5
10
There are 7 combos without dimes or quarters:
5+5+5+5+5+5
5+5+5+5+5
5+5+5+5
5+5+5
5+5
5
(32 pennies)
Total: 18 combos
