Y by Adventure10 and 4 other users
Hello AoPS,
I have decided to partner with 3 other AoPSers to run this tournament:
Professordad, Spring, and Soulspeedy.
Working in a similar manner as it would in real life.
Week 1: July 23-July 30
SIgnups, sample problems
Week 2: July 30-August 6
Mock AMC 10/Mock AMC 12
Week 3: August 7-August 14
Mock AIME
Week 4: August 15-August 22
Mock USA(J)MO
All contests will be released in this topic around 9 AM of the release date. You should turn in your submissions by 9 PM of the due date in a private message. This deadline may be pushed ahead an hour or two, but that's it (I mean you have a whole week, right?
). Qualifying scores/indexes will be posted within an hour of the deadline, and I will create them based on the performances. Preferably, I aim to have the AIME qualifying score through the AMC 10 be around 120 and for the 12 be around 100. Indexes to qualify for JMO should be around 190, and indexes to qualify for the USAMO should be around 220. However, this is all subject to change, as maybe the questions will be easier/harder than I may have thought.
Your job this week is to choose which one of the 10 or 12 you want to participate in. You can opt to do both, but in the end, if you qualify for both JMO and AMO, you are only eligible to take the mock USAMO. I will also post some sample/warmup problems (not that hard) to make sure this marathon doesn't die in its first week ).
I will post some general rules, most of which are the same as the official contests:
(Note: If you plan to do both, just put your name in both lists!)
I hope we have 30+ members. Note that there is no upper bound on the number of participants, and the deadline to sign up is at the end of this week (July 30, next Saturday). Also, post if you have any questions.
The top 2 winners will receive something mhy123 will decide later.
EDIT: mentioned some rules and stuff
EDIT2: changed +4 to +6
EDIT3: mentioned new additions
I have decided to partner with 3 other AoPSers to run this tournament:
Professordad, Spring, and Soulspeedy.
Working in a similar manner as it would in real life.
Week 1: July 23-July 30
SIgnups, sample problems
Week 2: July 30-August 6
Mock AMC 10/Mock AMC 12
Week 3: August 7-August 14
Mock AIME
Week 4: August 15-August 22
Mock USA(J)MO
All contests will be released in this topic around 9 AM of the release date. You should turn in your submissions by 9 PM of the due date in a private message. This deadline may be pushed ahead an hour or two, but that's it (I mean you have a whole week, right?
). Qualifying scores/indexes will be posted within an hour of the deadline, and I will create them based on the performances. Preferably, I aim to have the AIME qualifying score through the AMC 10 be around 120 and for the 12 be around 100. Indexes to qualify for JMO should be around 190, and indexes to qualify for the USAMO should be around 220. However, this is all subject to change, as maybe the questions will be easier/harder than I may have thought.Your job this week is to choose which one of the 10 or 12 you want to participate in. You can opt to do both, but in the end, if you qualify for both JMO and AMO, you are only eligible to take the mock USAMO. I will also post some sample/warmup problems (not that hard) to make sure this marathon doesn't die in its first week
).I will post some general rules, most of which are the same as the official contests:
(Note: If you plan to do both, just put your name in both lists!)
I hope we have 30+ members. Note that there is no upper bound on the number of participants, and the deadline to sign up is at the end of this week (July 30, next Saturday). Also, post if you have any questions.
The top 2 winners will receive something mhy123 will decide later.
EDIT: mentioned some rules and stuff
EDIT2: changed +4 to +6
EDIT3: mentioned new additions
This post has been edited 5 times. Last edited by mhy123, Aug 1, 2011, 9:01 PM
,
and 
are natural numbers coprime to each other. Find the remainder when 
is divided by 
.
be the two real roots to the equation 
,
and 
be the two non-real roots. Let 
and 
.
can be written in the form 
where 
and 
are integers and 
?
,
,
,
,
in such a way that 
is 1 unit away from 
,
is 1 unit away from 
,
is 1 unit away from 
.
where 
and 
are coprime to each other. Find 
.
denote the set of all fractions which are equal to![\[n\left(\frac{5}{6} - \sum_{k=4}^{1340} (-1)^k \cdot \frac{1}{k}\right)\]](http://latex.artofproblemsolving.com/4/9/5/4952d04bdeb7ce0a376972563ae9600a3fa4d115.png)
where 
.
is divided by 
)
