College and a math problem

Muirhead

United States556 Posts

April 03 2008 23:13 GMT

Harvard waitlisted me... It seems they rejected or waitlisted many of the top US mathematics students of the year (based on math competitions and Westinghouse). 9 of us are going to MIT

. I can't help but think Harvard shot itself in the foot.

Here's a problem easier than the last few I've posted:
Given a 1000x1000 chessboard, n squares are colored red and the rest are colored blue. I am not able to pick 3 red squares such that two of them are in different columns and (a possibly different) two of them are in different rows. What is the maximum possible value of n, with proof?

micronesia

United States24787 Posts

April 03 2008 23:20 GMT

How long would it take a computer program to calculate that by brute force? For me that would probably be the easier way haha.

Myxomatosis

United States2392 Posts

April 03 2008 23:30 GMT

is this an induction problem?

clazziquai

6685 Posts

April 03 2008 23:35 GMT

On April 04 2008 08:13 Muirhead wrote:
Harvard waitlisted me... It seems they rejected or waitlisted 7 of the top 10 US mathematics students of the year (based on math competitions and Westinghouse). 9 of us are going to MIT

Maximum possible value is OVER 9000! Proof? It's over 9000.....

WAIT

so you're one of the top 10 mathematicians in the USA? For high school students?

letsbefree

Canada123 Posts

April 04 2008 00:12 GMT

wow on Harvard waitlist...thats pretty fucking impressive

Daveed

United States236 Posts

April 04 2008 00:19 GMT

MIT math is better anyway =P

il0seonpurpose

Korea (South)5638 Posts

April 04 2008 00:19 GMT

Hey, its good to know you're smart but you don't have to be all cocky about how you're waitlisted and how harvard screwed up.

B1nary

Canada1267 Posts

April 04 2008 00:27 GMT

Congrats on getting into MIT. Even you don't go to Harvard, you can take courses there since the two are so close.

solution to problem?
+ Show Spoiler +

1000, all in one row or column. Suppose n=1001. By the pigeonhole thing, two rows must contain red squares and 2 columns must contain red squares. This allows you to pick 2 from different columns and 2 from different rows and it's gg. I suck at presenting proofs XD. I lost so many points in high school contests from crappy presentation, lol.

Zalfor

United States1035 Posts

April 04 2008 01:48 GMT

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the stupid answer seems like 1000. i don't see a better solution

raiame

United States421 Posts

April 04 2008 02:23 GMT

#10

I can't seem to find a different answer, but it seems too simple... >.< I suck at math.
Who would you say are the top 10? I'd like to say Haitao and Jacob Steinhardt are some <.< >.>

Slithe

United States985 Posts

April 04 2008 02:25 GMT

#11

I'm really surprised that Harvard is rejecting/waitlisting so many of the top math students. Then again, the college admissions process has always seemed quite mysterious to me. MIT's cooler anyway.

Muirhead

United States556 Posts

April 04 2008 02:54 GMT

#12

B1nary the point is that there must be 3 squares such that 2 are in the same row and 2 are in the same column. Your proof just shows that out of all the (much more than 3) red squares, two are in the same row and two are in the same column. Perhaps I'm misunderstanding something?

Raiame are you from TJ? Haitao and Jacob are both really really good and hardworkers too. I think Alex Zhai is the best in the class though. Haha you're not Haitao are you?

raiame

United States421 Posts

April 04 2008 02:56 GMT

#13

Yeah I am. Bah, I remember a time when I was better than Jacob at math <.< Haitao was always better than me although I beat him in state mathcounts >< Also, I never got into proofs, still short answer =[
Yeah Zhai's probably best.
Jacob's going to MIT, but I'm under the impression that Haitao's not sure yet.

Dromar

United States2145 Posts

April 04 2008 03:20 GMT

#14

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1000 ez.

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