Monday Math Madness #28: Monday Mac Madness Returns
16 Mar 2009 Quan Quach 10 comments 2,550 views
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.
The Answer
See the answer and winner here.
The Prize
The winner will receive a 10 dollar gift certificate to Amazon.com!
The Rules
- Email your answers to mondaymathmadness at gmail dot com.
- Inelgible for any one person to win more than once per year. But you should still submit your answer!
- Answer must be explained. You must show your work! We will accept answers in the form of a MATLAB script as well. We will be the final judge on whether an answer was properly explained or not.
- The deadline to submit answers is March 23rd 2009, Monday 11:59 PM Pacific Standard Time
- The winners will be chosen randomly from all the submittals using a random number generator.
- The winner will be announced at 9:00 AM PST March 27th, 2009.
- Comments for this post should only be used to clarify the problem. Please do not discuss ANY potential solutions.
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10 Responses to “Monday Math Madness #28: Monday Mac Madness Returns”
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Include MATLAB code in your comment by doing the following:
<pre lang="MATLAB">
%insert code here
</pre>
I would like some clarification about the problem:
Both laptops must be thrown at the same time and it counts as one iteration?, or you can throw one, see if it is broken, and then throw the other one, within the same iteration? or does it count as two iterations?
Regards
David
Do you mean how many iterations maximum, that is, is it possible to determine the floor before the max number of iterations is carried out?
@david
each time a laptop is dropped counts as one iteration.
@jewkulak
the idea is to find the algorithm that will work for all cases. this algorithm must also minimize the worst case scenario
its 4 or 5:D
may I say that Daniel is not that wise? I would have considered different the iteration “go to 36th floor” from the iteration “go to first floor”
(the sentence above is awful: I meant «I would have considered the iteration “go to 36th floor” different from the iteration “go to first floor”»)
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Are we to assume that there are 2 MacBooks, 3, or unlimited? i.e. the 2 that were originally sent, 3 “if I had two Green MacBooks at my disposal” plus Quan’s, or as many as they need but just need to find the algorithm that requires the fewest flights of stairs.
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