In 1961, faced with a troublesome cheating problem in the college mathematics classes I was teachng, I decided to use this problem as a "cheating tracer". I'll explain "tracer".

Physicians long have used injections of radioactive materials into the blod stream as a tracerfor flow through the body. A geiger counter outside the patient's body detected the radioactive material in its spread through the body.

To set up my "tracer", I gave a succinct treatment of the problem and its harmonic mean solution. I expected only my best students to understand, perhaps only one of them.

I deal with CHEATING by ASSIGNING EACH STUDENT A DIFFERENT FINAL EXAM PAPER -- SAME TYPE OF PROBLEMS, but DIFFERENT NUMBERS or LABELS in each VERION, and a DIFFERENT ORDERING OF THE PROBLEMS ON EACH PAPER. I also gave an "open-book exam". This is realistic, since "in real life" youmight consult a table of formulas. By not forcing the students to burden their memories, I coulld give difficult problems than is ordinarily done. If any student tried to copy a solutioon from the paper of another, she or he woudl be incorrect, because the numbers were different!

BUT I INSERTED THIS "FLYIING" PR0BLEM IN THE SAME FORM IN THE SAME POSITION ON ALL PAPERS.

GUESS WHAT? ALMOST EVERY ONE WROTE THE CORRECT SOLUTION FOR THIS PROBLEM. For many students, it was their OLY CORRETC SOLUTION.

THIS WAS CLEAR EVIDENCE THAT STUDENTS WERE SPREADING THE SOLUTION AROUND THE ROOM. I dind't know how. And didn't care, For, I didn't count this problem in the GRADING.

I joked that this was "evidence for telepathy".

This prolem also serves as an IGNORANCE TRACER.