TJUSAMO CONTEST #3 RESULTS - Thursday, December 14th, 2006

I. The raw scores:
Each problem is worth a total of seven math points. The score for each problem will also be multiplied by a style score, which is a multiple of 0.1 between 0 and 1. An X signifies that the solution for the problem was not received. If you receive a 0, then your styled score was replaced by your style multiplier.
ID--|-1-math/styled-|-2-math/styled-|-3-math/styled-|-total-math/styled---
01--|------0/0.7----|------0/0.9----|------0/0.7----|--------- 0/0.0 -----
02--|------0/0.6----|------0/0.6----|------X/X.X----|--------- 0/0.0 -----
03--|------0/0.7----|------0/0.7----|------X/X.X----|--------- 0/0.0 -----
04--|------0/0.7----|------X/X.X----|------X/X.X----|--------- 0/0.0 -----
05--|------0/0.8----|------0/0.6----|------0/0.7----|--------- 0/0.0 -----
06--|------X/X.X----|------0/0.7----|------X/X.X----|--------- 0/0.0 -----
07--|------0/0.6----|------0/0.6----|------X/X.X----|--------- 0/0.0 -----
08--|------1/0.7----|------0/0.8----|------0/0.9----|--------- 1/0.7 -----
09--|------X/X.X----|------0/0.8----|------X/X.X----|--------- 0/0.0 -----
10--|------X/X.X----|------X/X.X----|------1/0.7----|--------- 1/0.7 -----
11--|------0/0.7----|------3/1.8----|------2/1.4----|--(9th)-- 5/3.2 -----
12--|------X/X.X----|------1/0.6----|------0/0.7----|--------- 1/0.6 -----
13--|------0/0.5----|-----*6/4.2----|------0/0.7----|--(8th)-- 6/4.2 -----
14--|------0/0.7----|------0/0.8----|------0/0.7----|--------- 0/0.0 -----
15--|-----*7/5.6*---|------0/0.6----|------X/X.X----|--(2nd)-- 7/5.6 -----
16--|------0/0.7----|------0/0.7----|------X/X.X----|--------- 0/0.0 -----
17--|------0/0.7----|------0/0.6----|------0/0.6----|--------- 0/0.0 -----
18--|------0/0.3----|------0/0.6----|------X/X.X----|--------- 0/0.0 -----
19--|------3/1.8----|------0/0.7----|------X/X.X----|-(10th)-- 3/1.8 -----
20--|------0/0.8----|------0/0.8----|------0/0.7----|--------- 0/0.0 -----
21--|------0/0.4----|------0/0.7----|------X/X.X----|--------- 0/0.0 -----
23--|------X/X.X----|------0/0.7----|------0/0.3----|--------- 0/0.0 -----
24--|------0/0.7----|------0/0.8----|------X/X.X----|--------- 0/0.0 -----
26--|------X/X.X----|------0/0.8----|------1/0.7----|--------- 1/0.7 -----
27--|------X/X.X----|------4/2.8----|-----*3/2.1*---|--(6th)-- 7/4.9 -----
28--|-----*7/5.6*---|-----*6/4.8*---|-----*3/2.1*---|--(1st)--16/12.5-----
32--|------0/0.7----|------0/0.7----|------0/0.9----|--------- 0/0.0 -----
36--|-----*7/4.9----|------1/0.6----|------0/0.7----|--(5th)-- 8/5.5 -----
37--|-----*7/5.6*---|------0/0.6----|------0/0.7----|--(2nd)-- 7/5.6 -----
38--|------X/X.X----|------X/X.X----|------X/X.X----|--------- 0/0.0 -----
41--|------X/X.X----|------X/X.X----|------1/0.6----|--------- 1/0.6 -----
42--|------0/0.7----|------X/X.X----|------X/X.X----|--------- 0/0.0 -----
49--|------5/3.5----|------2/1.2----|------X/X.X----|--(7th)-- 7/4.7 -----
50--|-----*7/5.6*---|------X/X.X----|------X/X.X----|--(2nd)-- 7/5.6 -----
-Total contestants: 34
-Top 15 average: 3.7933


II. Score distributions:
Math|--#1--|--#2--|--#3--
7---|---5--|---0--|---0--
6---|---0--|---2--|---0--
5---|---1--|---0--|---0--
4---|---0--|---1--|---0--
3---|---1--|---1--|---2--
2---|---0--|---1--|---1--
1---|---1--|---2--|---3--
0---|--17--|--21--|--12--
X---|---9--|---6--|--16--

Note that for the following table, only solutions with positive math scores will be considered. The rest will be X's.
Style|--#1--|--#2--|--#3--
1.0--|---0--|---0--|---0--
0.9--|---0--|---0--|---0--
0.8--|---4--|---1--|---0--
0.7--|---3--|---2--|---5--
0.6--|---1--|---4--|---1--
0.5--|---0--|---0--|---0--
0.4--|---0--|---0--|---0--
0.3--|---0--|---0--|---0--
0.2--|---0--|---0--|---0--
0.1--|---0--|---0--|---0--
0.0--|---0--|---0--|---0--
X----|--26--|--27--|--28--


III. Overall awards:
-1st Place: Jacob Steinhardt(12.5)
-2nd Place Three Way Tie: Jimmy Clark, Mark Hou, Jonathan Wang(5.6)
-Honorable Mention(other person who solved a problem): Daniel Li(5.5)

IV. Other positive awards:
-Best solutions to problem #1(6.3): Jimmy Clark, Mark Hou, Jacob Steinhardt, Jonathan Wang
-Best solutions to problem #2(4.8): Jacob Steinhardt
-Best solution to problem #3(2.1): Sarah Marzen, Jacob Steinhardt
-Most interesting solution: Jacob Steinhardt (problem #3, you're getting too many of these awards =\, not sure if this actually works out though)
-Clearest: Jonathan Wang (problem #1)
-Most concise: Jacob Steinhardt (problem #2)
-Best rigor: Mark Hou(problem #1)
-Best diagram: Eric Bomgardner(problem #1)

V. Not positive awards:
-Most pages submitted: Allan Fan(6)
-Best BS(this was a hard award to decide!): Joseph Xu(composite+composite=composite (counterexample: 10+9=19))
-Most confusing: Ryan Brewster(problem #1, used determinants or something, but no explanation of methods, and I couldn't follow =/)
-Messiest: Jeff Chen 10(too much crossed out stuff, random car picture and wrote LANG: C++ on the top right =|)


VI. Comments:
-The average was rather low this time, lower than I expected. This may of been due to several factors: 1) Increased difficulty of receiving partial credit, 2) Problem #1 being geometry, 3) Less participants.
-Warning: Please reduce the number of BS proofs you turn in. If you think your proof will probably receive 0 points, it WILL receive 0 points. On a related note, hand waving and comical detractions in your proof generally reduce the grader's willingness to give you points.
-Note that TJUSAMO contests will always count for performance rankings; you don't need to ask.
-Problem #1: The formula [ABC]=absin(C)/2 is completely unnecessary. All you must notice is that the ratio of the area of two triangles which have equal altitudes to a base is equal to the ratio of the length of that base. Also, I think some of you thought that a quadrilateral having a circumcenter had to be a square. Well, that is BS.
-Problem #2: No fixed mod will work here. You must prove that a mod exists that will work for any a. Solving 20/21 of the cases will not earn any partial credit, as it does not significantly help the problem; you still have the same number of possible values for a, infinity. Also, some of you lost minor credit because you did not rigorously show that the desired mod exists. Also a lot of you tried to get partial credit by finding all the answers, but most of you forgot about the answer {2,1,2,0,0}.
-Problem #3: I have yet to find a solution that does not involve a bit of casework. However, some of you made the casework really messy and lost a little bit of style. I think the first step was the hardest part, realizing that there is exactly one 2 in the sequence, disregarding z_0.
-Difficulty levels of the three problems: #1 - mid AIME, #2 - really really easy USAMO, #3 - medium USAMO.
-Please learn to number your pages. A valid numbering would be {1/3, 2/3, 3/3}. Invalid numberings would be {1/1, 2/2} and {1/2}.
-Do NOT put your name on your paper! We are trying for anonymous grading similar to how the USAMO and most other olympiads are graded.
-Tip: Unlike the USACO, it is advantageous to fully solve one problem instead of making "observations" on all three problems. Also, it is beneficial to do the first problem first, as it is almost always the easiest (even if it is geometry).
-If you see an error, report it directly to Haitao, preferably via email.