Middle School Math Puzzle

Since there are middle school math parents and magazine editors among the core readership of this blog, I thought this might be interesting.

Keenan recently had a whole page of trapezoid area problems. Depending on how you approach it, you can get different answers, which I thought was a bit unfair. I'll explain what I'm talking about later, in case anyone wants to take a crack at it.

Traffic cone: important new findings

During Bernie and Isa's visit this weekend, Bernie and I took a stroll through the neighborhood that took us past the now well-known traffic cone. Close inspection revealed that the cone was, at one time, the property of St. Peter's Hospital, a half-mile to the east. While we now know that the cone was not left behind by a utility truck, unfortunately these new findings raise as many questions as they answer.

Isa's Riddle

Isa said to me, "Name a word that is both of two things, and yet also neither of the two things at the same time."
"I give up," I replied.
"Brunch," she said, "It's both breakfast and lunch, yet it is neither as well."

"Well, in that case," I said, "My new answer is spork. Not a spoon, not a fork. Both."

Best response gets an origami prize, made by Isa.

Four Card Puzzle

'Cause it's been awhile since we've had a good puzzle.

You're sitting at a table with four playing cards on it. Two are face up and two are face down. You see an 8, a King, a red-backed card, and a blue-backed card.

You're told that all the Kings in front of you have red backs. What is the maximum number of cards you have to turn over to test if that's true? Which cards do you turn over?

Simplify This

    (a+x)(b-x)(c+x)(d-x) ... (z-x)

"Simplify" means that the solution can be written using fewer characters than the problem itself uses.

factor this

x^4 - 11x^2 + 1

First prize is an Amazon gift certificate for one hundred dollars, decreasing in value by one dollar for each minute the problem remains unsolved. If it takes more than one hour forty minutes, you owe me money.

The Locker Puzzle

This is my favorite puzzle.

A hallway in a school has 100 lockers. A student runs down the hall and opens every locker. A second student runs down the hall and closes every other locker, starting at the second. A third student runs down the hall and "flips" every third locker, starting at the third - if the locker is open, he closes it; if it's closed, he opens it.

A total of 100 students run down the hall, opening and closing lockers. In general, the n-th student flips every n-th locker.

After all 100 students run through the hall, which lockers are open?