It is a new day.  Peace had been restored to the universe and with it has returned our beloved nickel.  In addition, a brand new, never-seen-before coin has been minted to celebrate the occasion:  the duodecidime—worth exactly twelve cents.  Show that  in  this  new age,  the  cashier’s  algorithm  using  quarters,  duodecidimes,  dimes,  nickels,  and  pennies  would not  always produce change using the fewest coins possible.