## Where to find resources on mathematical puzzles like this?

1) 6-sided die (sides: 1, 2, 3, 4, 5, 6), roll and win \$x depending on the side facing up. How much are you willing to pay to play this game?

2) If we play a game in which Player 1 picks a number 1-11, and then player 2 can add 1-11 to that (i.e. player 1 picks 5, player 2 can add to make it 6-16), what is the strategy to win this game if Player 1 wants to make 60?

Looking for a collection of similar questions or significantly challenging ones relative to these.

submitted by Nevin Manimala Nevin Manimala /u/letsgobaby

## Complex Analysis Summer Study Group?

Hey /r/math, I will be studying Gamelin’s Complex Analysis this summer in preparation for graduate school. While I enjoy studying immensely, I find that it can be a very lonely experience. Would anybody be interested in joining a study group? I was thinking we could create a google drive folder and submit our answers to problems and have a discord or whatsapp or something to discuss further. I would expect that you would know at least some real analysis, and would have a substantial amount of time to devote to solving problems. If I get at least five people interested I’ll start this up. You can comment or PM me.

submitted by Nevin Manimala Nevin Manimala /u/McTestes68

## Arzelà–Ascoli

Looking over my notes for real at the stuff I didn’t understand, Arzelà–Ascoli was the worst offender.

Wikipedia has a great article on it, but the proof they give (at least from what I can understand) isn’t general enough to deal with compact sets in abitrary metric spaces as opposed to just Rn.

Here are the two statements: Consider a sequence of real-valued continuous functions { fn }n ∈ N defined on a closed and bounded interval [a, b] of the real line. If this sequence is uniformly bounded and equicontinuous, then there exists a subsequence { fnk }k ∈ N that converges uniformly.

And the sequential version from my class: Let A be a compact set in a metric space (M, d), and suppose (fk) is a sequence of functions fk : A −→ R which is bounded and equicontinuous. Then (fk) has a uniformly convergent subsequence

Any help would really be apreciated

submitted by Nevin Manimala Nevin Manimala /u/sectandmew

## Social Dilemmas: Optimize the location of people in a room

While in a room of people, I thought of a problem involving a room of people. Unfortunately, I haven’t got a clue how to even begin solving it. I was curious to see if anyone could figure out a way to do so.

Suppose we have a rectangular 2d room, with a finite width and height of x and y. In this room, we must place n people. For each person, we must find a position in the room as well as a direction they’re facing.

The people have desire functions, and the goal is to try to optimize the positioning in the room so that the total desire sum is maximized. People are modeled as circles with radius 1. We’ll define the ‘face’ of a person as a single point on the perimeter. All circles must lie entirely within the room.

For every person, their total desire of a position + direction is based on the sum of their desire functions towards every other individual. And these desire functions depend on how well they can see other people.

A person can see someone else if there is a line between that person’s face and the other person’s circle that doesn’t intersect with any other circles. To be able to see someone, they must also be within a distance d (measured from face to the closest visible point).

The desire function for every individual to every one else is: if you can see them, then your desire is d-r, where r is the distance from their face towards the closest visible point on the others circle. If you can’t see them your desire is 0

As an example, here’s a simple drawing of an unoptimized room. https://puu.sh/AvaMd/d11bcc3e50.png The circles represent the people, the yellow dots their faces, and the red lines the available lines of sight.

Now how do I maximize the desires of the people in a room given some arbitrary x,y,n and r? If this generic case is too hard,you can replace all or some of these by constants. I recommend x=15, y=15, n=10,r=10

submitted by Nevin Manimala Nevin Manimala /u/FliesMoreCeilings