There are two specials at the Disgusting Diner: worms or cockroaches. You can order either one, prepared in one of three ways: charbroiled, deep-fried, or pickled. Six people are having lunch together. Everyone ordered one of the specials, but nobody ordered the exact same dish. Can you figure out who ate what?
- Either Cleo had worms or Dwayne had a pickled dish.
- Either Elyse had cockroaches or Fred had a deep-fried dish.
- Either Dwayne and Fred both had worms, or they both had cockroaches.
- Andrew and Cleo had their dishes prepared the same way.
- Bobbi did not have cockroaches.
- Elyse did not have a charbroiled dish.
- Dwayne did not have pickled cockroaches.
Scroll down for the answers!
By rule 5, we know Bobbi did not have cockroaches; she must have had worms. Suppose Andrew also had worms. By rule 4, since Cleo had her dish prepared the same way as Andrew’s, she must not have had worms; she had cockroaches. Then by rule 1, Dwayne had a pickled dish, and by rule 7 he did not have pickled cockroaches, so he must have had pickled worms. By rule 3, Fred also had worms. But this means four people had worms (Andrew, Bobbi, Dwayne and Fred), and since there are only three ways to prepare them, two of them must have had the exact same dish. This is not possible; therefore our original supposition was wrong, and Andrew did not have worms.
So, Andrew had cockroaches. By rule 4, Cleo had her dish prepared the same way as Andrew, so she must have had worms. We have now identified two people (Bobbi and Cleo) who had worms. By rule 3, Dwayne and Fred both had worms or they both had cockroaches; they couldn’t both have worms since that would mean a total of four people did, so they must have both had cockroaches. By process of elimination, Elyse had worms.
By rule 2, since Elyse did not have cockroaches, Fred must have had a deep-fried dish (cockroaches). Dwayne also had cockroaches but, by rule 7, not pickled ones, so he must have had charbroiled cockroaches. Andrew, the remaining person who had cockroaches, must have had pickled cockroaches. By rule 4, Cleo had her dish prepared the same as Andrew’s, so she had pickled worms. By rule 6, Elyse did not have a charbroiled dish, so she had deep-fried worms. The remaining diner, Bobbi, must have had charbroiled worms.
- Andrew had pickled cockroaches.
- Bobbi had charbroiled worms.
- Cleo had pickled worms.
- Dwayne had charbroiled cockroaches.
- Elyse had deep-fried worms.
- Fred had deep-fried cockroaches.
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