Math CentralQuandaries & Queries


Question from Jenny, a student:

Albert, Bernard, Charles, Daniel and Ellie play a game in which each is a frog or kangaroo. Frogs' statements are always false while Kangaroos' statements are always true. 1. Albert says that bernard is a kangaroo. 2. Charles says that Daniel is a frog. 3. Ellie says that Albert is not a frog. 4. Bernard says that Charles is not a kangaroo. 5. Daniel says that Ellie and Albert are different kinds of animals. How many frogs are there?

Hi Jenny,

I would analyze this problem by cases, starting with Daniel. I would start with Daniel because he says something about two of the others.

Case 1: Daniel is a kangaroo (tells the truth). Thus Ellie and Albert are different so there are two possibilities.

First possibility: Ellie is a frog and Albert is a kangaroo. Look at statement 3 "Ellie says that Albert is not a frog." But Ellie is a frog so this statement is false and Albert is a frog. But Albert is a kangaroo so this possibility is impossible.

Second possibility: Ellie is a kangaroo and Albert is a frog. Look at statement 3 again.

Case 2: Daniel is a frog and thus Ellie and Albert are not different. Again there are two possibilities. Examine each carefully.

Have fun with this,

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