Community

Want to learn how to tackle those tough MATHCOUNTS and AMC counting and probability problems? Check out Art of Problem Solving's Introduction to Counting & Probability by David Patrick.
Login Register Memberlist Search AoPS Blogs Contests Galleries Forum Index
The time now is Mon Nov 23, 2009 10:30 am
All times are UTC - 8
 		View posts since last visit
View unanswered posts
Home » High School Contests & Programs » Other US Contests & Programs » Mandelbrot
 
Mandelbrot 2009-2010
Post new topic   Reply to topic View previous topicView next topic
15 Posts • Page 1 of 1
Author Message
pinkmuskrat
Yang-Mills Theory
Yang-Mills Theory


Offline
Joined: 28 Dec 2008
Posts: 602
Location: a sucky state....
Taiwan, Province of ChinaMonaco
To rate posts you must be logged in
#1
Mandelbrot 2009-2010
discussion and results
This year's Mandelbrot Competition has gotten under way. Good Luck everyone! Also remember not to discuss rounds until the testing window is over. Smile

mandelbrot.org/
_________________
Star Wars !MATH=AOPS!
Mandelbrot Round 1 UNMPNM Round 1 Mandelbrot Round 2
....YaY #1 aLcUmUs...YaY 1337 gAmEs In FtW...

PostPosted: Wed Nov 04, 2009 5:52 pm  Back to top 
  ProfilePMWWW
athunder
Riemann Hypothesis
Riemann Hypothesis


Offline
Joined: 30 Mar 2008
Posts: 415
Location: Michigan...to be exact...look down the window
IndiaUnited States
To rate posts you must be logged in
#2
I believe the last day allowed to take it is November 8th? I geuss we can discuss scores and what not on November 9th.
_________________
MY GOALS: DONT FAIL. 17/50 MMPC II, 25/25 AMC 8, 25/25 MOEMS, 70/80 COMC, Make Nats, 150 AMC 10, 7 AIME Mandelbrot R1=10/14

PostPosted: Thu Nov 05, 2009 4:00 am  Back to top 
  ProfilePMBlog
varunrocks
Riemann Hypothesis
Riemann Hypothesis

Offline
Joined: 25 Dec 2007
Posts: 272
To rate posts you must be logged in
#3
can we now discuss the solutions or are people still taking the test.

PostPosted: Mon Nov 09, 2009 4:47 pm  Back to top 
  ProfilePM
athunder
Riemann Hypothesis
Riemann Hypothesis


Offline
Joined: 30 Mar 2008
Posts: 415
Location: Michigan...to be exact...look down the window
IndiaUnited States
To rate posts you must be logged in
#4
i dont think so...i have heard something about a "2 week period" so..maybe another week.
_________________
MY GOALS: DONT FAIL. 17/50 MMPC II, 25/25 AMC 8, 25/25 MOEMS, 70/80 COMC, Make Nats, 150 AMC 10, 7 AIME Mandelbrot R1=10/14

PostPosted: Mon Nov 09, 2009 5:08 pm  Back to top 
  ProfilePMBlog
darkdieuguerre
Riemann Hypothesis
Riemann Hypothesis

Offline
Joined: 09 Nov 2007
Posts: 304
Location: Maryland
To rate posts you must be logged in
#5
Quote:
"Students should refrain from discussing the contest problems until Monday following the end of the official testing week."


Well, the testing week ended on Sunday. Therefore, we wait until the Monday after, which is next Monday, November 16th? It would be nice to have an explicit notification on when we can discuss problems, because there is ambiguity, since most of the testing week was last week.
_________________
10^{12} pins make a terrapin.

PostPosted: Mon Nov 09, 2009 5:18 pm  Back to top 
  ProfilePM
JBL
Birch & Swinnerton Dyer
Birch & Swinnerton Dyer

Offline
Joined: 04 Jul 2003
Posts: 10748
Location: Brooklyn, NY or Cambridge, MA
United States
To rate posts you must be logged in
#6
Why don't you send an e-mail to Sam Vandervelde and ask for clarification? Rolling Eyes
_________________
Joel
Hi Deeps! <3

PostPosted: Mon Nov 09, 2009 5:36 pm  Back to top 
  ProfilePMWWW
pinkmuskrat
Yang-Mills Theory
Yang-Mills Theory


Offline
Joined: 28 Dec 2008
Posts: 602
Location: a sucky state....
Taiwan, Province of ChinaMonaco
To rate posts you must be logged in
#7
darkdieuguerre wrote:
Quote:
"Students should refrain from discussing the contest problems until Monday following the end of the official testing week."


Well, the testing week ended on Sunday. Therefore, we wait until the Monday after, which is next Monday, November 16th? It would be nice to have an explicit notification on when we can discuss problems, because there is ambiguity, since most of the testing week was last week.


I'm pretty sure the "Monday" being referred to is November 9th. Also, results are posted on the website tomorrow.
_________________
Star Wars !MATH=AOPS!
Mandelbrot Round 1 UNMPNM Round 1 Mandelbrot Round 2
....YaY #1 aLcUmUs...YaY 1337 gAmEs In FtW...

PostPosted: Mon Nov 09, 2009 5:48 pm  Back to top 
  ProfilePMWWW
xpmath
Birch & Swinnerton Dyer
Birch & Swinnerton Dyer

Offline
Joined: 19 Mar 2007
Posts: 2915
Location: Michigan
IndiaUnited States
To rate posts you must be logged in
#8
Results are up now, you know...

I didn't take round 1, so this is the fourth year in a row I won't be taking all the Mandelbrot rounds.
_________________
Udonis the friendly whale.

PostPosted: Mon Nov 09, 2009 5:51 pm  Back to top 
  ProfilePM
not_trig
Navier-Stokes Equations
Navier-Stokes Equations


Offline
Joined: 30 Apr 2006
Posts: 1587
Location: NORTH CAROLINA!
United States
To rate posts you must be logged in
#9
uhh those definitely aren't all the results... lots of schools are missing. (No Enloe!)
_________________
RSI '09. Goals: 35 USAMO, IMO, ILO.

PostPosted: Mon Nov 09, 2009 5:59 pm  Back to top 
  ProfilePMAIMBlog
pinkmuskrat
Yang-Mills Theory
Yang-Mills Theory


Offline
Joined: 28 Dec 2008
Posts: 602
Location: a sucky state....
Taiwan, Province of ChinaMonaco
To rate posts you must be logged in
#10
Mandelbrot posts the results at the stated time (or earlier i guess?!). Those are the results. However, not all the schools have submitted their results yet, and the scoreboard will be later updated accordingly.
_________________
Star Wars !MATH=AOPS!
Mandelbrot Round 1 UNMPNM Round 1 Mandelbrot Round 2
....YaY #1 aLcUmUs...YaY 1337 gAmEs In FtW...

PostPosted: Mon Nov 09, 2009 6:56 pm  Back to top 
  ProfilePMWWW
BOGTRO
Birch & Swinnerton Dyer
Birch & Swinnerton Dyer


Offline
Joined: 29 Jun 2006
Posts: 3138
Location: Somewhere Rating: 1337
United States
To rate posts you must be logged in
#11
Sorry, but where are the results?
_________________
My own chess quotes:
~Chess is not about winning... until you lose~
~The best time to search for alternatives is when you calculate that there are none~

PostPosted: Tue Nov 10, 2009 9:09 am  Back to top 
  ProfilePMBlog
pinkmuskrat
Yang-Mills Theory
Yang-Mills Theory


Offline
Joined: 28 Dec 2008
Posts: 602
Location: a sucky state....
Taiwan, Province of ChinaMonaco
To rate posts you must be logged in
#12
Go to mandelbrot.org/ and then look on the left side of the site. Under the heading of "Scorecenter", click "Results". There is then a link to national level results, and you can click on the map for regional results.
_________________
Star Wars !MATH=AOPS!
Mandelbrot Round 1 UNMPNM Round 1 Mandelbrot Round 2
....YaY #1 aLcUmUs...YaY 1337 gAmEs In FtW...

PostPosted: Tue Nov 10, 2009 11:48 am  Back to top 
  ProfilePMWWW
Differ
Riemann Hypothesis
Riemann Hypothesis


Offline
Joined: 01 Sep 2007
Posts: 354
Location: California
To rate posts you must be logged in
#13
So how do you solve #7 in a reasonable timeframe?

PostPosted: Thu Nov 12, 2009 2:29 pm  Back to top 
  ProfilePM
pinkmuskrat
Yang-Mills Theory
Yang-Mills Theory


Offline
Joined: 28 Dec 2008
Posts: 602
Location: a sucky state....
Taiwan, Province of ChinaMonaco
To rate posts you must be logged in
#14
Doesn't seem like there's a solution yet.

The largest discussion on AoPS so far:
http://www.artofproblemsolving.com/Forum/viewtopic.php?t=311057
_________________
Star Wars !MATH=AOPS!
Mandelbrot Round 1 UNMPNM Round 1 Mandelbrot Round 2
....YaY #1 aLcUmUs...YaY 1337 gAmEs In FtW...

PostPosted: Thu Nov 12, 2009 2:45 pm  Back to top 
  ProfilePMWWW
math154
Birch & Swinnerton Dyer
Birch & Swinnerton Dyer


Offline
Joined: 21 Jan 2008
Posts: 3509
Location: St. Louis, MO
United States
To rate posts you must be logged in
#15
I came up with a casework method during the competition which seemed nice at first but unfortunately requires some stuff which makes it not appealing.

Solution
Let each row have 1609 squares and each column have 2009 squares. Set up position (a,b) for column a and row b, so they start at (1,1) and end at (1609,2009). Now consider the intersection points of red and green (a,b). The back and forth movement motivates casework on parity.

First we note the following (consider moves as including (1,1) and (a,b)):

  • if b is odd, then red moves (b - 1)1609 + a = 1609b + a - 1609 squares
  • if a is odd, then green moves (a - 1)2009 + b = 2009a + b - 2009 squares
  • if b is even, then red moves (b - 1)1609 + (1610 - a) = 1609b - a + 1 squares
  • if a is even, then green moves (a - 1)2009 + (2010 - b) = 2009a - b + 1 squares.

Now we equate and do ugly stuff. Sad

Case 1: a odd, b odd.
2009a + b - 2009 = 1609b + a - 1609\implies2008a = 400 + 1608b \\ \implies251a = 201b + 50\implies50a\equiv50\pmod{201} \\ \i...
Because a is odd, a = 402n + 1, so b = 502n + 1, for 5 solutions when n = 0,1,2,3,4 (remember 1\le a\le1609 and 1\le b\le2009).

Case 2: a odd, b even.
2009a + b - 2009 = 1609b - a + 1\implies2010a = 1608b + 2010 \\ \implies5a = 4b + 5\implies a\equiv1\pmod4 \\ \implies a = 4n...
Because a is odd, a = 8n + 1 so b = 10n, and there are 200 solutions for when 1\le n\le200.

Case 3: a even, b odd.
2009a - b + 1 = 1609b + a - 1609\implies1610b = 2008a + 1610 \\ \implies805b = 1004a + 805\implies805b\equiv805\pmod{1004} \\...
Because b is odd, b = 2008n + 1 so a = 1610n and there are 0 solutions for this case.

Case 4: a even, b even.
2009a - b + 1 = 1609b - a + 1\implies2010a = 1610b \\ \implies201a = 161b\implies40a\equiv0\pmod{161} \\ \implies a = 161n.
Because a is even, a = 322n and b = 402n for 4 solutions when n = 1,2,3,4.

Thus we have 5 + 200 + 0 + 4 = \boxed{209} solutions in all.


So many places for screwing up...

PostPosted: Thu Nov 12, 2009 3:01 pm  Back to top 
  ProfilePMAIMBlog
Display posts from previous:   Sort by:   
15 Posts • Page 1 of 1
Post new topic   Reply to topic View previous topicView next topic
Home » High School Contests & Programs » Other US Contests & Programs » Mandelbrot
 
Jump to:  


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum
You cannot attach files in this forum
You can download files in this forum
You cannot post calendar events in this forum


© Copyright 2008 AoPS Incorporated. All Rights Reserved. • Foundation • Privacy • Contact Us