blinkdagger

Hello everyone, we have a brand new contest rolling over at Sol's blog wildaboutmath.com!

This time around The Art of Problem Solving folks have donated several $25 gift certificates that can be used in their bookstore! I believe they have a few international distributors as well. I encourage you to check out their site. The authors range from talented math wizards that obtain the sole perfect score on the American High School Mathematics Examination (AHSME), members of numerous academic Olympiad teams, and won numerous trophies. Now they want to help young kids to obtain those dreams too. From the site:

We were the kids who wanted to win the trophies. We worked hard and became the kids who won the trophies. The trophies are in attics now. The problem-solving skills, the love of mathematics, and the friendships forged with peers with similar interests remain. We've applied the skills we've developed through mathematics to a variety of fields in college, then in the professional world.

Now we've returned to our starting point - the student in a room, chewing on a pencil, staring at a question, giving up, reading the answer, and thinking. . . This time you are the student. We are building this site for you, to provide a resource you can turn to.

Now head on over to Sol's new Monday Math Madness Challenge. If you decide to submit an answer, please state if you were referred by blinkdagger. We're trying to keep some simple logistics on how things are panning out.

Another Contest for MATLABers

For those faithful MATLAB readers of our blog, a new MATLAB contest just came out today. Encourage you all to take a look at their 17th contest: Wiring Circuits. You don't need to know anything about circuitry. All you need to know is how to connect dots the most efficient way under certain constraints. The contest runs for 7 days.

Monday Mac Madness was the most successful contest we have conducted to date. In total, we received 103 submissions, which is twice as many as our original goal of 50. And since we received more than 50 submissions, we chose two winners for this contest!

Congratulations to Raymond Chong and Allan Wong for winning Monday Math Madness #4!

The Answer is 7!

The answer to the problem is 7. The two most common answers we received were 11 and 6. Some of the explanations were very clear and succinct while some of you struggled to explain your strategy.

Since the personnel at Blinkdagger are too lazy (or dumb) to write up a solution, they have instead chosen to explain the answer by choosing some of the best submissions. One of the clearest explanations came from Greg Zeigler, shown below:
"It would take 7 iterations to determine the three fastest macbooks. I'll include a visualization as well since this is tough for me to explain properly.

First, make five groups of five and run each group through 1 iteration. Discard the slowest two of each group since there are at least three machines faster than them.

Run an iteration using the fastest macbook from each group. Discard the two slowest, as well as the other two laptops remaining in each of their groups. Then go to the group that had the third fastest and discard the second and third laptops since they are slower than a macbook which is slower than at least two others.

For the same reason, you can discard the third laptop from the group whose laptop was second in the sixth iteration. You know that the first laptop from the sixth iteration (being the fastest of the fastest) is the fastest laptop you have, so you can set it aside. This leaves you with 5 laptops, enough for one more iteration.

The first laptop from the seventh iteration is the second fastest, the second is the third fastest, and as I already said the fastest laptop is the first laptop from the second iteration."

Another great explanation can be found here by Janet (the Geekmom).
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This is the fourth post in the blinkdagger signal processing series.

Introduction

In the previous tutorial, we showed you how correctly scale your x-axis so that your FFT results were meaningful. In this post, we will be discussing zero-padding, a method that can help you better visualize/interpret your fft results. Zero-padding means that you append an array of zeros to the end of your input signal before you fft it. Luckily, the fft command within Matlab makes it very easy to zero-pad.

Why Zero Pad?

Two reasons that you might want to zero pad is to increase the number of data points to a power of 2. Traditionally, the FFT algorithm is more efficient when it is dealing with signals that contain 2^N data points. Nowadays, this isn't as important with the modern algorithms. Another reason for zero-padding is for a "better" resolution in the frequency spectrum. We'll discuss why quotes are used around better in a bit. In general, zero-padding can prove quite useful and should be used when using the fft command. In practice, it is helpful to zero pad a signal to 4 times it's original length, giving you a 4-fold increase in the frequency resolution.
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In Depth Car Buying Guide by Chanlee Sutoyo. She is a proud owner of a 2008 Nissan Altima. She shares with us some useful tips in buying a new car.

Buying a new car can be a stressful and nervewracking experience, but with the right information and strategy, you can get a great deal without even setting foot in a showroom. I recently bought my first new car, a 2008 Nissan Altima, for $1340 under invoice, and in this post I will show you how I did it.

I don’t usually obsess over products that I buy, but this being the biggest purchase I’ve ever made, I was determined not to be a victim. We’ve all heard horror stories of unscrupulous dealers who cheat you out of your hard-earned money. So I began with some Google searches.

Several searches quickly revealed CarBuyingTips.com and Fighting Chance as the best advice sites, and Yahoo!Autos and Edmunds as the best pricing and data sites.
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Photo from jarkko

The Contest Problem

Daniel: Hey Quan, we just received a shipment of 25 Macbook Pros from Apple Inc.

Quan: WOWIE PAZOWIE! What are we going to do with 25 Macbook Pros?

Daniel: Let's keep 3 of them for personal use and give the other 22 away to the winner of this contest.

Quan: Okay. But personally, I think the winner would rather prefer a 10 dollar GC to amazon.

Daniel: You're probably right. In that case, we'll just take a sledgehammer and smash the other 22 laptops to oblivion. Anyhow, since all Macbook Pros are not created equally, let's determine which 3 Macbook Pros are the fastest. Those are the one's that we'll keep.

Quan: Good idea. We can go to the computer lab and run a simple test.

Daniel: Right. We can hook them up to the blinkdagger station and have each laptop process a special algorithm that I developed in MATLAB.

Quan: But we can only hook up 5 Macbook Pros at one time. And the station only ranks the 5 laptops from 1 (fastest) to 5 (slowest). It doesn't give us any other information. This could potentially take forever!

Daniel: Don't worry Quan. The optimal strategy will only take ______ iterations.

How many iterations do Quan and Daniel have to run to determine which 3 Macbooks are the fastest?

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