Extreme examples and counterexamples

I recently read this puzzle at the Futility Closet and it reminded me of a technique that I like to use to test conjectures (when possible). I don’t know if it has a name, so I’ll call it “looking for extreme examples and counterexamples.” I like this technique because when it works it is fast and…

Is or an inclusive or or an exclusive or?

(That was a fun title to write!) At the start of our discrete mathematics course we talk about symbolic logic. Students are often confused by the logical operator “OR.” If p and q are statements then p OR q is true if either p is true or q is true or if both p and…

Euathlus and Protagoras

In my Discrete Mathematics class we discussed a few famous paradoxes, such as Russell’s paradox/barber paradox/librarian paradox, the liar’s paradox, and the naming numbers paradox. Afterward, a student of mine shared with me this old legal paradox featuring Euathlus and Protagoras. Euathlus wanted to become a lawyer but could not pay Protagoras. Protagoras agreed to…