Question 29214: Suppose a country has only two denomination of coins: $0.05 coins and $0.07 coins. Determine all monetry values that can be obtained using only coins.
Answer by bmauger(101)   (Show Source):
You can put this solution on YOUR website! 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.
For instance 106=26 + 80 = three seven cent pieces + (1 + 16) nickels...
 (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)
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.
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