The following problem appeared in The Bent Winter 2010 issue. (The Bent is a publication of Tau Beta Pi, and Engineering Honor Society.)
Al's job is testing bowling balls. He has two identical bowling balls and is to test their impact resistance by dropping them out of windows on various floors of a 100-story building. He is to determine from which exact floor a dropped ball will shatter on impact with the pavement below. Al knows nothing about the strength of the balls. They may shatter when dropped from the first floor or not until dropped from the 100th floor. What is the minimum number of ball drops needed to guarantee that Al can uniquely determine the floor fro which the balls will shatter. Balls that do not shatter may be dropped again. Both balls may be destroyed during the test. Include a brief outline of how testing is done.This problem raises questions and metaquestions.
- What is the answer?
- A while back I had an undergrad work on the general problem of f floors and e eggs (we used eggs not bowling balls). Hence I know the answer with matching upper and lower bounds for all f and e. Should I submit my answer? If I did would I be a ringer? All you get for submitting a correct solution is your name in the next issue so that would be okay(?). Even so, its seems like cheating. (See here for my students paper. We didn't publish it since a similar paper had already appeared: The Egg Drop Number by Michael Boardman, Mathematics Magazine, Vol 77, No. 5, Ded 2004, 368-372. You can find it here.)
- When is one a ringer? In a later issue there was a problem I had not seen before but was able to solve easily with graph theory. For that problem am I a ringer?
- The intent of the problems (I think) is to test your cleverness not your repository of knowledge. With this in mind, clearly if I send in a solution to the Bowling Ball problem, I am being a ringer. For the graph theory problem it is less clear.
- Once in a restaurant I was doing the kids math puzzles on the paper placemats with my great nieces and nephews. There was one problem that I could solve by brute force but tried instead to find a clever solution (there probably wasn't one). Hence I could not solve it. Or at least that is what my great nieces and nephews think. This might be called being a reverse-ringer. Is there a better term?
Here is a problem from
Activity book from the NSA on Codes, Ciphers, Puzzles)
that is geared towards kids. I was able to do every puzzle in it
very quickly except this one.
If you know the answer please tell me
before some kid asks me:
Logic Puzzle Number 1: If a railroad train is moving northward, there is a part of each car on the train that is moving southward at each instant, no matter how fast the train is going. what is the contrary piece moving southward? Hint- sketch a train moving on a track and examine the parts you sketch.