# Boreholes

**by [Matt Hall](https://github.com/kwinkunks)**

You have a list of boreholes. Each one has an (x, y) location. The locations are given as a Python string, and look like this:

    ..., (12.1, 34.3), (56.5, 78.7), (90.9, 12.1),...
    
Your data, when you receive it, will be longer than this.
    
We're going to analyse these locations. We need the answers to the following questions:

1. How many boreholes are there? We'll call this number _n_.
2. What's the distance, **to the nearest metre** between the first two boreholes in the list?
3. What is the mean straight-line distance between all pairs of boreholes **to the nearest metre**? Call this _m_.
4. There is a clump of boreholes. How many boreholes are in the clump? (A borehole is defined to be in a clump if the mean distance to its nearest _n_ / 5 neighbours is _m_ / 4 or less.)

Please note that all your answers must be integers. If you get a float for an answer, round it.


## Example

Here are the locations of some boreholes:

      (1, 4), (5, 4), (9, 3), (2, 8), (6, 4), (9, 9), (5, 5), (4, 3), (4, 5), (2, 1)
      
If we plot them, they look like this:

    y
    ^
    9 - - - - - - - - - 0
    8 - - 0 - - - - - - -
    7 - - - - - - - - - -
    6 - - - - - - - - - -
    5 - - - - 0 0 - - - -
    4 - 0 - - - 0 0 - - -
    3 - - - - 0 - - - - 0
    2 - - - - - - - - - -
    1 - - 0 - - - - - - -
    0 - - - - - - - - - -
      0 1 2 3 4 5 6 7 8 9 > x
    
Here's how we'd answer the questions for this small dataset:

- In this example, there are **10** wells (marked `0` on the plot above).
- The distance between the first two boreholes in the list, (1, 4) and (5, 4), is **4**.
- The mean distance between boreholes is 4.58... which to the nearest metre is **5**.
- There are **4** wells in the clump. See below.

Wells in the clump are marked `X` here (the borehole marked `O` does not meet the criterion):

    y
    ^
    9 - - - - - - - - - 0
    8 - - 0 - - - - - - -
    7 - - - - - - - - - -
    6 - - - - - - - - - -
    5 - - - - X X - - - -
    4 - 0 - - - X X - - -
    3 - - - - O - - - - 0
    2 - - - - - - - - - -
    1 - - 0 - - - - - - -
    0 - - - - - - - - - -
      0 1 2 3 4 5 6 7 8 9 > x


## A quick reminder how this works

This document is formatted in [Markdown](https://daringfireball.net/projects/markdown/).

You can retrieve your data, which is always a string, by choosing a **`<KEY>`** (also a string). This ensures that you have different data from other people, so be creative. 

```
url = 'https://kata.scienxlab.org/challenge/boreholes'
params = {
    'key': <KEY>  # Replace <KEY> with your own string.
}
r = requests.get(url, params)
r.text
```

To answer question 1, change the `params`:

```
params = {
    'key': <KEY>,   # Use the same key you used to get your input.
    'question': 1,
    'answer': 1234  # Your answer; can be a float, int, list or array;
                    # the challenge description will tell you which.
}
```

To get a hint for a question, provide the question number but no answer:

```
params = {
    'question': 1,
}
```

[Complete instructions at kata.scienxlab.org](https://kata.scienxlab.org/challenge)

[An example notebook to get you started](https://gist.github.com/kwinkunks/50f11dac6ab7ff8c3e6c7b34536501a2)

----

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