In 2000 I made up and graded the following problem from the Maryland Math Olympiad from 2007 (for High School Students)
There are 2000 cans of paint. Show that at least one of the following two statements is true:It was problem 1 so it was supposed to be easy 95% of the students got it right and I suspect everyone reading this blog can do it. Note that the students taking this exam, Part II of a math olympiad, did well on part I, so they are good students. (Part I is 25 TOUGH multiple choice questions, point off if you are wrong, and Part II is 5 problems that require proofs.)
- There are at least 45 cans of the same color.
- There are at least 45 cans of all different colors.
I got two funny answers:
ANSWER ONE: Paint cans are grey. Hence there are all the same color. Therefore there are 2000 cans that are the same color.
ANSWER TWO: If you look at a paint color really really carefully there will be differences. Hence, even if two cans seem to both be (say) RED, they are really different. Therefore there are 2000 cans of different colors.Were they serious?
The first one points to a problem with the phrasing of the question- I clearly did not mean the cans themselves, and all of the other students knew that, but looking at the problem it could be interepreted that way. This person might have been serious.
The second one I can't imagine was serious.