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College and a math problem

Blogs > Muirhead
Post a Reply
Muirhead
Profile Blog Joined October 2007
United States556 Posts
Last Edited: 2008-09-04 02:13:52
April 03 2008 23:13 GMT
#1
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?

****
starleague.mit.edu
micronesia
Profile Blog Joined July 2006
United States24710 Posts
April 03 2008 23:20 GMT
#2
How long would it take a computer program to calculate that by brute force? For me that would probably be the easier way haha.
ModeratorThere are animal crackers for people and there are people crackers for animals.
Myxomatosis
Profile Blog Joined July 2006
United States2392 Posts
April 03 2008 23:30 GMT
#3
is this an induction problem?
clazziquai
Profile Blog Joined October 2007
6685 Posts
April 03 2008 23:35 GMT
#4
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 . 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?


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?


#1 Sea.Really Fan / #1 Nesh Fan / Terran Forever~
letsbefree
Profile Blog Joined January 2008
Canada123 Posts
April 04 2008 00:12 GMT
#5
wow on Harvard waitlist...thats pretty fucking impressive
hehe...
Daveed
Profile Blog Joined December 2006
United States236 Posts
April 04 2008 00:19 GMT
#6
MIT math is better anyway =P
il0seonpurpose
Profile Blog Joined January 2007
Korea (South)5638 Posts
April 04 2008 00:19 GMT
#7
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
Profile Blog Joined January 2008
Canada1267 Posts
April 04 2008 00:27 GMT
#8
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
Profile Blog Joined October 2005
United States1035 Posts
April 04 2008 01:48 GMT
#9
+ Show Spoiler +
the stupid answer seems like 1000. i don't see a better solution
555, kthxbai
raiame
Profile Joined December 2007
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
Profile Blog Joined February 2007
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
Profile Blog Joined October 2007
United States556 Posts
Last Edited: 2008-04-04 02:56:05
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?
starleague.mit.edu
raiame
Profile Joined December 2007
United States421 Posts
Last Edited: 2008-04-04 02:58:06
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
Profile Blog Joined June 2007
United States2145 Posts
April 04 2008 03:20 GMT
#14
+ Show Spoiler +
1000 ez.
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