My physics professor loves giving little logic puzzles at the end of our homework...
This weeks was “Sheila is a cashier at a convenience store and has run out of one-dollar bills, but she has plenty of coins - pennies, nickels, dimes, and quarters. She always gives the change with the fewest possible coins. The change she just gave a customer contained 20 coins. What is the minimum possible value of the change?”
I’m asking this question here because a friend and I are disagreeing as to what the answer should be. Our general strategy is the same: we start by saying she gave 20 pennies since this is the least possible value of 20 coins. Then we note that this is impossible because Sheila wouldn’t give more than 4 pennies because she could just give a nickel instead (condition of least coins given). So now we have Sheila giving 4 pennies and 16 nickels. But this can’t be either because she would never give more than a nickel since she could just replace 2 nickels with a dime. And so on...but we’re getting a bit confused and have dissenting opinions when it comes to the dimes.
Could someone help us out here?