# Map sheets

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

You might want to get a cup of coffee before reading this one.

We have a list of locations in Canada, given to 'quarter unit' accuracy. The locations use a highly esoteric addressing system, based on Canada's [National Topographic System](https://en.wikipedia.org/wiki/National_Topographic_System), and are accurate to about ±200 m or so, because each quarter unit is about 1/4 mile, or 400 m, on each side. In this exercise, we'll assume it is 400 m exactly.

Each location has two parts, separated by a `'/'`:

    a-71-L/15-I-89
    ^^^^^^ ^^^^^^^
     unit / sheet
    
The `unit` part gives the **quarter-unit** (a, b, c, or d), followed by the **unit** (1 to 100), followed by the **block** (A to L).

The `sheet` part gives the **map sheet** (1 to 16), followed by the **map area** (A to P), followed finally by the **map** (a 2-digit number).

In other words, it reads a bit like a postal address, starting with small-scale features (the quarter unit) and working up to a 'map', which measures hundreds of km along one side.

The tricky part is that, within each block type, the sub-blocks are labeled in very particular ways. All of them begin in the lower-right corner, but then they become quite idiosyncratic. This figure illustrates the relationships, **but the figure is not to scale** so don't read too much into it.

<img src="https://kata.scienxlab.org/static/nts.svg">


## Questions

Can you answer the following questions about this dataset:

1. How many map sheets contain **two or more** locations?
2. Look at the first location in your list. Find the **index** of the column that this location appears in, at each scale; **start with the map scale** and end with the quarter-unit scale. Submit a string representing a comma-separated sequence of indices.
3. What is the x-coordinate of the centre of the quarter-unit represented by the **first** location in your list?
4. Considering _only the blocks in your list_, which of them is **closest to the centroid** (mean central point) of all the locations in your list? Call this position **C**.
5. **Bonus question!** What is the full NTS 'address' of the quarter-unit **containing the centroid, C**? You must format your string exactly as in your input data.

You do not have to solve question 5 to get the key for the next challenge.


## Rules and assumptions

- Use the lower-left corner of map 97 as the origin for coordinates.
- Assume the smallest entity, the quarter-unit, is 400 m on a side.
- Your answers should be strings or integers. Note that the solution to question 2 should be a string like `"2,1,3,3,0,0"`.
 

## Example

Here are three locations:

    c-70-H/16-K-77,b-41-I/08-D-87,a-74-D/16-K-77
   
We'd answer the questions as follows:

1. There is **`1`** unique map sheet with at least two locations, **`"16-K-77"`**.
2. The first location appears in the 3rd column, i.e. column index 2, at the map scale (`77`), the index 1 column at the map area scale (`K`), the index 3 column at the map sheet scale (`16`), etc. The correct reponse is **`"2,1,3,3,0,0"`**. 
3. The first location is at (1272200, 277400) so the answer is (to the nearest metre) **`1272200`**.
4. The mean location is (1055000, 196866.667) and of the three blocks given, the block which is the shortest distance from this is **`"a-74-D/16-K-77"`**.
5. The mean location is in block **`"a-62-A/04-L-77"`**. Note that this block is not in your list.


## 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/map-sheets'
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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