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Muirhead
United States557 Posts
 . 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 States24808 Posts
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Myxomatosis
United States2392 Posts
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clazziquai
6685 Posts
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?  | ||
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letsbefree
Canada123 Posts
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Daveed
United States236 Posts
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il0seonpurpose
Korea (South)5638 Posts
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B1nary
Canada1267 Posts
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. | ||
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Zalfor
United States1035 Posts
the stupid answer seems like 1000. i don't see a better solution | ||
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raiame
United States421 Posts
Who would you say are the top 10? I'd like to say Haitao and Jacob Steinhardt are some <.< >.> | ||
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Slithe
United States985 Posts
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Muirhead
United States557 Posts
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? | ||
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raiame
United States421 Posts
Yeah Zhai's probably best. Jacob's going to MIT, but I'm under the impression that Haitao's not sure yet. | ||
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Dromar
United States2145 Posts
1000 ez. | ||
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