Inter-Divisional+Topics

=**Essner Finals Practice**= UM posts all of the previous Essner preliminary round "exams", preliminary round solutions, and final round "exams", but they do //not// for some reason post the solutions to the final round tests. So, that leaves it to us to compile our own list of answers/solutions for future generations of RE mathletes to have! If you do some problems from an old essner final exam, you have the opportunity to be a part of this effort!

To save a ton of time, I recommend scanning the answers instead of typing them all out (//especially// the proofs). Having work on there is nice as well!

-Btw, for everyone who took the 2011-12 preliminary test, the solutions (with short explanations) are up here - I highly recommend checking out how they did questions you found challenging.
 * ~  ||~   ||~ ==Ransom Everglades Essner Solutions Database== ||~   ||
 * Year || Test || "Potential Solution" uploads (we could use more than one per test) || Comments/Questions/Disagreements ||
 * 2012 || [[file:Essner 2012 Pic 1.bmp]] ||  ||   ||
 * 2011 || Essner 2011 ||  ||   ||
 * 2010 || [[file:Essner 2010.doc]] ||  ||   ||
 * 2009 || [[file:Essner 2009.doc]] ||  ||   ||
 * 2008 || [[file:Essner 2008.docx]] ||  ||   ||
 * 2007 || [[file:Essner 2007.doc]] ||  ||   ||
 * 2006 || [[file:Essner 2006.doc]] ||  ||   ||
 * 2005 || [[file:Essner 2005.doc]] || [[file:Essner 2005 Matt's Solutions.PDF]]: Attempts 1a), 1b1), 2a), 3), 4), and 5a)-5b) || Sorry, typo on part 4 of mine, should say "Given", not "Give" -Matt M ||
 * 2004 ||  ||   ||   ||

Number Theory!
-Check out Modular Arithmetic, for a place to start! It is simple to learn but hard to master... super useful and pretty interesting! We're working on posting problems and a more condensed explanation up here soon.



Combinatorics!
In the below document is what this guy named Professor Benjamin calls "The 12-Fold Way of Combinatorics" - basically a table that lays out how to answer almost any type of "basic" combinatorial question the Essner could throw at us. A lot of combinatorial questions can be rephrased as, "How many ways can I place //x// amount of candies in //y// bags?" - whether the candies are people, colored balls, or integers and the bags are committees, buckets, or other groupings. If a bunch of the cells don't make sense, that's all right - we can figure them out together! =) Btw, does anyone know what Stirling numbers are? -Matt

A decent but pretty dense resource on more combinatorics: Counting Objects in Boxes

Practice problems! Also, please feel free to download, add to, and re-upload this problems document ^ if you find any more worth working on! =)

Musings on the Essner Test!
>Out of what I have seen, most tests are set up the following way:

+Two number theory problems (divisibility/mod and random stuff they pull from Hubert knows where) +One precal-esque problem (sequences, velocity, etc) +One geometry problem +One probability problem (often involving games or random walks)

But they often change it up by swapping some of these out for unclassifiable, quirky little problems, so expect to be surprised =) Matt



Crazy, Challenging, Inter-Divisional Problems!
The //**ultimate**// resource for taking on non-FAMAT tests like the Essner and the AIME with confidence and dignity.

Or, one day it will be. Hopefully.


 * To be continued...**