Three friends – Cecilia, Emilee, and Nicole – all work at the Super Duper Market after school each day. They either stock shelves or they bag the customers’ groceries at the cash register. Each day Ms. Seeger, the store manager, decides which friend will do which job by these rules:
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Either Cecilia or Nicole, but not both, will stock shelves;
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If Cecilia stocks shelves, then Emilee will bag groceries;
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Emilee and Nicole will not both bag groceries.
Which of the three friends could have stocked shelves yesterday AND could be bagging groceries today?
Solution
Let’s look at the friends one at a time. We’ll start with Cecilia.
Suppose Cecilia stocked shelves yesterday. Then, from (1), Nicole did not, so Nicole bagged groceries. Also, from (1), Emilee bagged. But, from (3), Emilee and Nicole can’t both bag. So, Cecilia couldn’t have stocked shelves yesterday – or any day, for that matter! She’ll always be bagging groceries.
So much for Cecilia. Then, from (1) Nicole must always stock shelves.
So, is Emilee the one who can either bag groceries or stock shelves? From (2), if Cecilia stocks, then Emilee will bag. But nothing is said about when Cecilia doesn’t stock (which is always); Emilee can bag whether Cecilia stocks or not. So far so good! Now, can Emilee stock shelves? No problem: Emilee and Nicole can’t both bag groceries, but nothing says they can’t both stock shelves.
So, Cecilia will always bag groceries, Nicole will stock shelves, and Emilee can do either, presumably depending on where Ms. Seeger needs her more. Emilee is the one who could have stocked shelves yesterday and could be bagging groceries today.
Ms. Seeger, by the way, could simplify her rules. Seriously.