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Trust Bruno or Not?

A former student suggested this week's problem. It also provides a shift from the other types of problems being offered.

Three friends of ours, Ablie, Bruno, and Clarence, all have strange habits.

One of them always lies.

One of them always tells the truth.

One of them alternates between telling the truth and telling lies.

We overheard Ablie and Clarence make the following statements...

Ablie: "I am a liar."

Clarence: "Ablie does not alternate between a lie and the truth."

Can you determine whether or not to believe what Bruno tells you?

My student M.L.'s note: Mathematics has so much more to offer students than the understanding of numbers or the repetition of calculations. The roots of mathematics are Logic and Reasoning, and each of these elements are critically important to students in how they go about problem solving. The skills the student learns about problem solving can be taken into the 'real world' and can help the individual solve other problems they may encounter. It is in this way that math can be taken out of the classroom and tied closely to our everday living....This problem is a Reasoning type problem that involves enough different elements to make it interesting but not too many to make it unsolvable."


Source: M.L. (Former WWU Student)

Hint: Suppose Albie always lies...or always tells the truth...or alternates....then....


Solution Commentary: Bruno says you can solve this problem on your own....!