A new coin that is worth exactly 4 cents has been add to our currency system. Prove or disprove the statement: "The cashier`s algorithm using quarters, dimes, nickels, 4 cent coins, and pennies and...

A new coin that is worth exactly 4 cents has been add to our currency system. Prove or disprove the statement: "The cashier`s algorithm using quarters, dimes, nickels, 4 cent coins, and
pennies and will always produce change using the fewest coins possible."