## Sunday, April 01, 2012

### Trick question or Stupid question?

April fool days Blogs or Columns may

present an open problem as closed,

present a closed problems as open,

make us wonder if it's a joke or not, (Lance STILL isn't telling!), or

make us question some well held beliefs.

This year I will take a different route- similar to what Lipton did here, which is NOT try to fool you, but present a post ABOUT tricky or foolish or odd things.

When is a trick question a stupid question? I give some examples and my opinions. But I want your opinions- are these questions (with the answers I give) TRICK QUESTIONS or STUPID QUESTIONS?
1. How many states are in the United States? Answers and Commentary
2. What is the least common Birthday in America? Answers and Commentary
3. What is the degree of (x-a)(x-b)(x-c)... (x-z)? Answers and Commentary
4. What US state has the eastern most point in America? Answers and Commentary
5. What is the least common first names for a U.S. President? (The answer is a tie.) Answers and Commentary
6. Which two numbers come at the end of this sequence?
2,4,6,30,32,34,36,40,42,44,46,50,52,54,56,60,62,64,x,y
7. An expert on tracking animals notices one day that there are bear tracks and rabbit tracks converging on the same spot. He can estimate that they converged at 6:00PM with a margin of error of 17 seconds. Hence they must have been there at the same time. He also notices that from the spot they converged only rabbit tracks can be found. HOW CAN A RABBIT EAT A BEAR FOR DINNER? Answers and Commentary
8. There are 6 blue socks, 8 white socks, and 10 black socks in a drawer. How many do you need to take out of the drawer in order to get a pair. Answers and Commentary
9. What is the square root of nine? Give the answer as an anagram of the question. Answers and Commentary

1. Googling, I find there is no legal difference between a state and a commonwealth; they are just two different names for the same thing.

2. I thought the trick answer to number 8 was 2.

3. My opinions on a few of the questions:
1. The answer should be 50. Stupid question.
3. Very interesting trick question, brings up all kinds of issues of type safety and lack of specificity in mathematics/education. Also, there's an argument to be made that the degree of the zero polynomial should be negative infinity, not zero.
8. Stupid question. If you're going to be that obtuse about reading the question I think you could argue for answers 2 (you need 2 socks), 4 (to make sure you get 2 of the same color) or 22 (to leave one pair).

4. Perhaps a clever question is one where the trick solution is unique (namely, there is only one "nice" solution), whereas in a stupid question you can come up with a ton of trick solutions that are just as clever (or stupid). I think number 8 is particularly stupid, it doesn't even say in the question that you own the socks, only that they are in a drawer, so the trick solution is not even correct...

By the way, my answer to 7 would be "it is 6pm now and the bear is still there" (I think most bears don't eat rabbits anyway, so the rabbit must have just kept going).

5. Obama's first name is Barack, not Barak.

6. I have fixed the socks problem so the only answers are 0 or 4. I think
its a STUPID question since it hinges on the definition of `has'
and does not bring out any math points of interest.

I have fixed Obamas first name.

I agree that (x-a)(x-b)...(x-z) question is interesting.

The sequence question I really can't tell if its a trick or stupid.
I couldn't get it and the answer delighted me, so I"LL call it a trick,
though there are those that disagree.

7. The socks problem still has another valid solution: 2. If you want a pair of socks of the same color, just get a pair out of the drawer. That was my initial answer.

8. Dilbert asks Dogbert an exceptionally tricky question today … a question that I cannot recall ever seeing acknowledged, much less constructively answered, anywhere in the STEM blogosphere/literature.

9. Regarding the (x-a)(x-b)...(x-z) question, I agree with the mentioned person who argued that the two "x" symbols are really different. The first x is a parameter and the second is a variable. Or, in the context of a computer program, the first x is a global variable and the second x is a redundant name for a (different) local variable.

10. Regarding (x-a)(x-b)...(x-z): It is not that clear that the zero polynomial has zero degree. Often it is said to be minus infinity, so that deg(pq)=deg p + deg q works.