Advent Calendar 2015 Introduction

Following the fun that was hopefully had from last year's Advent Calendar I am making another one this year!

If you are unsure of what an Advent Calendar is here is a short explanation; to celebrate Christmas many shops sell Advent Calendars. For every day of December up to Christmas these calendars have a small treat which is normally a piece of chocolate.

But of course, why not have a math problem instead? That is exactly what I have decided to do. The problems will be of varying difficulty and like last year I will try to post the problems on the previous day to account for the time zone difference.

Please have fun and I hope you enjoy solving the problems!

Here is a link to the set.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in $</span> ... <span>$ or $</span> ... <span>$ to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

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Advent Calendar 2015 Introduction

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including olympiad champions, researchers, and professionals.