Day 6 - Readme with answers

Author: romellem

6/README.md

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+# Answers
+
+| Part 1 | Part 2 |
+|--------|--------|
+|   4233 |  45290 |
+
+## --- Day 6: Chronal Coordinates ---
+
+The device on your wrist beeps several times, and once again you feel like you're falling.
+
+"Situation critical," the device announces. "Destination indeterminate. Chronal interference detected. Please specify new target coordinates."
+
+The device then produces a list of coordinates (your puzzle input). Are they places it thinks are safe or dangerous? It recommends you check manual page 729. The Elves did not give you a manual.
+
+_If they're dangerous,_ maybe you can minimize the danger by finding the coordinate that gives the largest distance from the other points.
+
+Using only the [Manhattan distance](https://en.wikipedia.org/wiki/Taxicab_geometry), determine the _area_ around each coordinate by counting the number of [integer](https://en.wikipedia.org/wiki/Integer) X,Y locations that are _closest_ to that coordinate (and aren't _tied in distance_ to any other coordinate).
+
+Your goal is to find the size of the _largest area_ that isn't infinite. For example, consider the following list of coordinates:
+
+    1, 1
+    1, 6
+    8, 3
+    3, 4
+    5, 5
+    8, 9
+    
+
+If we name these coordinates `A` through `F`, we can draw them on a grid, putting `0,0` at the top left:
+
+    ..........
+    .A........
+    ..........
+    ........C.
+    ...D......
+    .....E....
+    .B........
+    ..........
+    ..........
+    ........F.
+    
+
+This view is partial - the actual grid extends infinitely in all directions. Using the Manhattan distance, each location's closest coordinate can be determined, shown here in lowercase:
+
+    aaaaa.cccc
+    aAaaa.cccc
+    aaaddecccc
+    aadddeccCc
+    ..dDdeeccc
+    bb.deEeecc
+    bBb.eeee..
+    bbb.eeefff
+    bbb.eeffff
+    bbb.ffffFf
+    
+
+Locations shown as `.` are equally far from two or more coordinates, and so they don't count as being closest to any.
+
+In this example, the areas of coordinates A, B, C, and F are infinite - while not shown here, their areas extend forever outside the visible grid. However, the areas of coordinates D and E are finite: D is closest to 9 locations, and E is closest to 17 (both including the coordinate's location itself). Therefore, in this example, the size of the largest area is _17_.
+
+_What is the size of the largest area_ that isn't infinite?
+
+-----------------
+
+## --- Part Two ---
+
+On the other hand, _if the coordinates are safe_, maybe the best you can do is try to find a _region_ near as many coordinates as possible.
+
+For example, suppose you want the sum of the [Manhattan distance](https://en.wikipedia.org/wiki/Taxicab_geometry) to all of the coordinates to be _less than 32_. For each location, add up the distances to all of the given coordinates; if the total of those distances is less than 32, that location is within the desired region. Using the same coordinates as above, the resulting region looks like this:
+
+    ..........
+    .A........
+    ..........
+    ...###..C.
+    ..#D###...
+    ..###E#...
+    .B.###....
+    ..........
+    ..........
+    ........F.
+    
+
+In particular, consider the highlighted location `4,3` located at the top middle of the region. Its calculation is as follows, where `abs()` is the [absolute value](https://en.wikipedia.org/wiki/Absolute_value) function:
+
+*   Distance to coordinate A: `abs(4-1) + abs(3-1) =  5`
+*   Distance to coordinate B: `abs(4-1) + abs(3-6) =  6`
+*   Distance to coordinate C: `abs(4-8) + abs(3-3) =  4`
+*   Distance to coordinate D: `abs(4-3) + abs(3-4) =  2`
+*   Distance to coordinate E: `abs(4-5) + abs(3-5) =  3`
+*   Distance to coordinate F: `abs(4-8) + abs(3-9) = 10`
+*   Total distance: `5 + 6 + 4 + 2 + 3 + 10 = 30`
+
+Because the total distance to all coordinates (`30`) is less than 32, the location is _within_ the region.
+
+This region, which also includes coordinates D and E, has a total size of _16_.
+
+Your actual region will need to be much larger than this example, though, instead including all locations with a total distance of less than _10000_.
+
+_What is the size of the region containing all locations which have a total distance to all given coordinates of less than 10000?_