## Intel day 3 March 13, 2010

Posted by Akhil Mathew in General.
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(Today was the third day of the Intel STS competition.)

I had my third judging interview today at about 11:40 am.   The judging panel included a computer scientist who pointed to the seven wrapped chocolates on the desk and informed me that to each was assigned a number, and that I needed to discover which contained the median. I didn’t have the actual numbers, but I could compare any two.  In the end, I said something about $O(n \log n)$ sorting algorithms (e.g. heapsort).  He then asked me about counting paths from (0,0) to (m,n) where one can move either right or up on each move; I stated a recursive formula, but got the wrong closed form expression (it’s a binomial coefficient, and I said it was a power of 2).  I was then asked by the other judge about what change I would make if I had to design the human body.  I suggested eliminating cognitive biases and improving rationality but that wasn’t legal; I then suggested various ideas such as removing vestigial organs and improving our ability to type, but settled on increasing the efficiency with which energy can be extracted from food.

I then had lunch and went to the National Academy of Sciences, where we set up our projects.   My poster had developed a slight tear from being sent through the mail, but I fixed it with construction paper.

1. Qiaochu Yuan - March 13, 2010

Let me tell you about one of _my_ judging questions, at which I failed miserably. Suppose you are on a boat holding a bowling ball in the middle of a lake. You throw the bowling ball overboard so that it lands in the water. Has the water level risen or fallen? Has the level of your boat relative to the shore risen or fallen?

Akhil Mathew - March 14, 2010

Either someone was asked recently about the situation for ice floating in water that melts- does the water level change?
In your case, since the bowling ball displaces mass while in the boat and volume when sunk in the water, the water level will have fallen after the bowling ball sinks (since its density is greater than that of water). The level of the boat should, I think, decrease (?).

Having not taken physics in three years, I’d probably have been unable to answer that question if I had it (and without the benefit of that earlier conversation).

Qiaochu Yuan - March 15, 2010

Yep, that sounds right. I botched the application of Archimedes’ principle to this question; it was awful. The ice question is an important one to understand, though – it’s important to understand that floating ice melting doesn’t contribute at all to rising sea levels.

2. lifeofpi - April 17, 2010

I’ve always been confused about this floating ice melting question. Isn’t it true, though, that the density of freshwater is less than the density of saltwater and hence, floating freshwater ice (for instance, the ice sliding from glaciers to the sea) melting will indeed cause the sea level to rise?

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