Wild About Math! Making Math fun and accessible

21Mar/090

MMM #28: You have a few more days to submit your answer

You have until Monday night at midnight to submit your answer to MMM #28 at Blinkdagger.

Here's the problem:

The Problem Statement

Daniel: Hey Quan, we just received a shipment of the latest Green MacBook Pros from Apple Inc. Unfortunately, they heard about what we did to the last shipment, so they only sent 2 this time. One for you, and one for me.

Quan: Hm, what are you going to do with your laptop?

Daniel: Well, I just moved into a new apartment complex that is 36 stories high. I’ve always pondered how durable these Green MacBooks really are. And I was wondering what the highest floor is from which I can drop this MacBook, and still have it operational . . .

Quan: Well, since you only have one MacBook, you could start at the first floor. If you drop it there, and it doesn’t break, you can move on up to the second floor. Using this method, you can work your way up to the 36th floor. The worst case scenario is that it could take 36 iterations, but eventually you’ll find out the highest floor that the MacBook can survive from!

Daniel: Yes, I could do that, but my apartment complex doesn’t have an elevator, and I would get tired of running up and down the stairs all day. Now, if I had two Green MacBooks at my disposal, I could perform this task in a much more efficient manner.

Quan:

Daniel: Don’t worry Quan, I have it all figured out. In the worst case scenario, it will only take us ____ iterations to figure out what the highest floor is!


How many iterations do Quan and Daniel have to perform to determine the highest floor that a Green MacBook can be dropped and still be operational?

You may assume the following:

  • A MacBook that survives a fall can be used again.
  • A broken MacBook must be discarded.
  • The effect of a fall is the same for all MacBooks.
  • If an MacBook breaks when dropped, then it would break if dropped from a higher window.
  • If an MacBook survives a fall, then it would survive a shorter fall.
  • It is not ruled out that the first-floor windows break MacBooks, nor is it ruled out that the 36th-floor windows do not cause a MacBook to break.
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