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PillowGit authored Mar 20, 2024
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# Internet Connection

March madness has started and everything is going perfectly as planned! (minus some issues with the coding questions...) Because you're such an amazing organizer and the lovely people at ACM
offer so much support, the event is far more popular than anyone could have imagined. It's nearly time to host the hackathon, and you're beginning to realize that it's almost impossible to pack
everyone into the Computer Science building for this event. The concern now is, where can we put students on campus so that they still have access to a strong internet connection throughout the hackathon?

Thankfully, you managed to get a list of all the locations of available routers on campus, as well as how far they can reach. The list of all routers may look something like the following:
```
Router located at x=4, y=7 with reach=3ft
Router located at x=6, y=4 with reach=4ft
Router located at x=10, y=10 with reach=3ft
```
Imagining the campus as a grid on a cartesian plane, we can picture where the routers are. Unfortunately for us however, the school cheaped out when buying routers. They opted for a large
quantity of routers with bad service, but long range.

A single router is not enough for a student to maintain a stable connection. To combat this while remaining cost effective, the school has implemented a system where two routers can help boost
each others signals and offer a student a stable connection!

Now, if a student is within range of two different routers at once, their connection will be more than enough to do sustain any activities they may try. Our goal is to ensure that every
student has a stable connection for this hackathon, so we will only look for areas that are in range of 2 different routers to try and place them there.

## Part 1

Given the long list of routers, **how many pairs of routers offer an area of any size where a student can maintain a stable connection?**

## Part 2

To avoid scattering students all over campus in search of good internet connection, we have to optimize our space. We have all the spaces where students have a good internet connection now,
we just need to figure out where the students should go. **What is the largest area of overlap that any pair of routers creates?**

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