Frances has some coins in her purse. She sees that she can’t make exactly one dollar with them. When she adds up all her coins she sees that she gets the largest total possible without being able to make exactly one dollar.
What coins does she have?
Solution
Frances has one 50c piece, and four 20c pieces.
Here is how we can work it out:
She can't have two 50c coins because they would make $1. So she can only have one 50c coin.
If she had five 20c pieces she could make a dollar, so she can only have four 20c pieces. That means that she can’t have a 10c piece, because 50c plus 2x20c plus 10c would make $1.
Extension:
What is the largest number of coins that Frances can have and not make up exactly one dollar?