For the Win! on Brilliant

I've been playing a lot of For the Win! on Art of Problem Solving recently, and I wanted to see if I could make something similar on Brilliant. So I created this problem set. This set has $20$ questions that I encountered in a round of FTW. See how you can do!

$\textbf{Some Rules}$

The basic rules of the game are simple. Solve the problems as fast as you can in a $45$ second time limit. Time yourself. If there are $n$ players in a game, then the $k$ th person to get a question right gets $n-k+1$ points. The person with the most points at the end wins.

When you are solving a problem, have the page open on Brilliant and keep track of your answers and times in a chart on your paper. When you have finished the questions, input your answers into the questions on Brilliant. If you got a question wrong, then move on. Do NOT attempt the problem again and re-time yourself. Mark an X on your table (or something similar, just make sure you know you got it wrong). Then when you are done, input your times into the other note in this set, following the instructions there. I will update the chart there for at least a week for two.

I prefer to time myself with Online Stopwatch. Be sure to record your times if you want to go against me and whoever else has participated! Please time yourself to $\textbf{two decimal places}$ . You are permitted to take off $1$ second from your time per question to account for switching between pages/tabs to get to the timer.

On the other note in this set, I will post the results and the point totals. That is also the place for you to input your times.

Good luck to all of you, and have fun! Feel free to ask any questions you have below!

Up to $20$ people can participate in this contest. If there are already $20$ people in it, you can still attempt the problems. Here is a list of all participants.

Note: I do not in any way claim to have created any of these problems. All problems come from Art of Problem Solving.

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 `\(` ... `\)` or `\[` ... `\]` 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}`	$\boxed{123}$

For the Win! on Brilliant

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