Question 708509
Regardless of knowledge of any counting principles, you should just use your logical common cents.  Only pennies and dimes.  


Can 34 cents be made using only pennies? Yes.  Need 34 pennies.
Can 34 cents be made using only dimes? No.  3 dimes is not enough and 4 dimes is too much, cents.  


Start then with the dimes.
Use 0 dimes.  How many pennies are needed?
Use 1 dime.  How many pennies are needed?
Use 2 dimes.  So how many pennies?
Use 3 dimes; how many pennies?


Those were 4 different ways to make 34 cents using only pennies and dimes. (or should that be said, "pennies or dimes"?)