SEARCH HOME
 Math Central Quandaries & 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,
Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.