Question 29214
Start with your 5 cent piece. With it by itself you can come up with the values (in pennies) of:
5, 10, 15, 20, 25... etc. e.g. all values divisible by 5 can be paid for.
Now with a 7 cent piece and three five cent pieces you can come up:
7, 12, 17, 22, 27
And with two 7 cent pieces and two nickels you can come up with:
7, 14, 19, 24 
Three 7-cent pieces & a nickel you can come up with:
7, 14, 21, 26 
Four 7-cent pieces...
7, 14, 21, 28 
Now looking at the list you'll see that we have values of:
24=two seven cent pieces and two nickels
25=five nickels
26=three seven cent pieces and one nickel
27=one seven cent piece and four nickels AND
28=four seven cent pieces
Since that covers 5 numbers in a row (24 through 28) you can create every number above by adding more nickels to one of the five numbers.<br>
For instance 106=26 + 80 = three seven cent pieces + (1 + 16) nickels...
{{{3(7)+17(5)=21+85=106}}} (Granted there might be other ways to get to 106, but the point is we can get to any value adding nickels to one of these combinations)<br>
So you can make every number above 24 cents, plus all the other numbers listed:
Your answer then is:
5, 7, 10, 12, 14, 15, 17, 19, 20, 21, 22, and 24 and above.