meetforever/GRPO_CL huggingface dataset:
user: This will probably be a little series :)

X-Shape

You will get an odd Integer n (>= 3) and your task is to draw a X. Each line is separated with '\n'.

Use the following characters:  ■ □

For Ruby, Crystal and PHP:   whitespace and o 

e.g.:



                                     ■□□□■
            ■□■                      □■□■□
  x(3) =>   □■□              x(5)=>  □□■□□
            ■□■                      □■□■□
                                     ■□□□■


 Series: ASCII Fun

ASCII Fun #1: X-Shape
ASCII Fun #2: Funny Dots
ASCII Fun #3: Puzzle Tiles
ASCII Fun #4: Build a pyramid

Answer: {"fn_name": "x", "inputs": [[3], [7]], "outputs": [["\u25a0\u25a1\u25a0\n\u25a1\u25a0\u25a1\n\u25a0\u25a1\u25a0"], ["\u25a0\u25a1\u25a1\u25a1\u25a1\u25a1\u25a0\n\u25a1\u25a0\u25a1\u25a1\u25a1\u25a0\u25a1\n\u25a1\u25a1\u25a0\u25a1\u25a0\u25a1\u25a1\n\u25a1\u25a1\u25a1\u25a0\u25a1\u25a1\u25a1\n\u25a1\u25a1\u25a0\u25a1\u25a0\u25a1\u25a1\n\u25a1\u25a0\u25a1\u25a1\u25a1\u25a0\u25a1\n\u25a0\u25a1\u25a1\u25a1\u25a1\u25a1\u25a0"]]}
user: Your goal in this kata is to implement a difference function, which subtracts one list from another and returns the result.

It should remove all values from list `a`, which are present in list `b`.

```python
array_diff([1,2],[1]) == [2]
```

If a value is present in `b`, all of its occurrences must be removed from the other:

```python
array_diff([1,2,2,2,3],[2]) == [1,3]
```
~~~ if:c
NOTE: In C, assign return array length to pointer *z
~~~

Answer: {"fn_name": "array_diff", "inputs": [[[1, 2], [1]], [[1, 2, 2], [1]], [[1, 2, 2], [2]], [[1, 2, 2], []], [[], [1, 2]]], "outputs": [[[2]], [[2, 2]], [[1]], [[1, 2, 2]], [[]]]}
user: # The Problem

Dan, president of a Large company could use your help. He wants to implement a system that will switch all his devices into offline mode depending on his meeting schedule. When he's at a meeting and somebody texts him, he wants to send an automatic message informing that he's currently unavailable and the time when he's going to be back.

# What To Do

Your task is to write a helper function `checkAvailability` that will take 2 arguments:

* schedule, which is going to be a nested array with Dan's schedule for a given day. Inside arrays will consist of 2 elements - start and finish time of a given appointment,

* *currentTime* - is a string with specific time in hh:mm 24-h format for which the function will check availability based on the schedule.
  * If no appointments are scheduled for `currentTime`, the function should return `true`. If there are no appointments for the day, the output should also be `true`
  *  If Dan is in the middle of an appointment at `currentTime`, the function should return a string with the time he's going to be available.
  
  
# Examples
`checkAvailability([["09:30", "10:15"], ["12:20", "15:50"]], "11:00");`
should return `true`

`checkAvailability([["09:30", "10:15"], ["12:20", "15:50"]], "10:00");`
should return `"10:15"`

If the time passed as input is *equal to the end time of a meeting*, function should also return `true`.
`checkAvailability([["09:30", "10:15"], ["12:20", "15:50"]], "15:50");`
should return `true`

*You can expect valid input for this kata*

Answer: {"fn_name": "check_availability", "inputs": [[[["09:30", "10:15"], ["12:20", "15:50"]], "10:00"], [[["09:30", "10:15"], ["12:20", "15:50"]], "11:00"], [[["09:30", "10:15"], ["12:20", "15:50"]], "10:15"], [[], "10:15"], [[["12:13", "23:50"]], "10:15"], [[["12:13", "23:50"]], "23:55"], [[["12:13", "23:50"]], "17:43"]], "outputs": [["10:15"], [true], [true], [true], [true], [true], ["23:50"]]}
user: The purpose of this series is developing understanding of stastical problems in AS and A level maths. Let's get started with a simple concept in statistics: Mutually exclusive events.

The probability of an OR event is calculated by the following rule:

`P(A || B) = P(A) + P(B) - P(A && B)`

The probability of event A or event B happening is equal to the probability of event A plus the probability of event B minus the probability of event A and event B happening simultaneously.

Mutually exclusive events are events that cannot happen at the same time. For example, the head and tail results of a toin coss are mutually exclusive because they can't both happen at once. Thus, the above example for a coin toss would look like this:

`P(H || T) = P(H) + P(T) - P(H && T)`

Note that the probaility of tossing a coin and the result being both head and tails is 0.

`P(H || T) = (0.5) + (0.5) - (0)`
`P(H || T) = 1`

Thus the probability of a coin toss result being a heads or a tails is 1, in other words: certain.


Your task:

You are going to have to work out the probability of one roll of a die returning two given outcomes, or rolls. Given that dice rolls are mutually exclusive, you will have to implement the above forumala. To make this interesting (this is a coding challenge after all), these dice are not fair and thus the probabilites of receiving each roll is different.

You will be given a two-dimensional array containing the number each of the results (1-6) of the die and the probability of that roll for example `[1 , 0.23]` as well as the two rolls for example `1` and `5`. 

Given the two roll probabilities to calculate, return the probability of a single roll of the die returning either. If the total probability of the six rolls doesn't add up to one, there is a problem with the die; in this case, return null. 
Return your result as a string to two decimal places.

Example below:

`1 : 1/6`

`2 : 1/6`

`3 : 1/6`

`4 : 1/6`

`5 : 1/6`

`6 : 1/6`

If asked for the rolls `1` and `2` then you would need to sum the probabilities, both `1/6` therefore `2/6` and return this. As above, you will need to return it as a decimal and not a  fraction.

Answer: {"fn_name": "mutually_exclusive", "inputs": [[[[3, 0.4], [4, 0.1], [1, 0.01], [2, 0.09], [5, 0.2], [6, 0.1]], 1, 6], [[[1, 0.1], [2, 0.14], [3, 0.16], [4, 0.2], [5, 0.15], [6, 0.25]], 1, 4], [[[1, 0.6], [2, 0.1001], [3, 0.0999], [4, 0.1], [5, 0.05], [6, 0.05]], 3, 4], [[[6, 0.25], [1, 0.1], [3, 0.16], [2, 0.14], [5, 0.15], [4, 0.2]], 1, 6], [[[3, 0.4], [4, 0.1], [1, 0.01], [2, 0.09], [5, 0.2], [6, 0.2]], 1, 6]], "outputs": [[null], ["0.30"], ["0.20"], ["0.35"], ["0.21"]]}
user: # Task
 The year of `2013` is the first year after the old `1987` with only distinct digits.

 Now your task is to solve the following problem: given a `year` number, find the minimum year number which is strictly larger than the given one and has only distinct digits.

# Input/Output


 - `[input]` integer `year`

 `1000 ≤ year ≤ 9000`


 - `[output]` an integer

  the minimum year number that is strictly larger than the input number `year` and all its digits are distinct.

Answer: {"fn_name": "distinct_digit_year", "inputs": [[1987], [2013]], "outputs": [[2013], [2014]]}
user: Let us begin with an example:

A man has a rather old car being worth $2000. 
He saw a secondhand car being worth $8000. He wants to keep his old car until he can buy the secondhand one.

He thinks he can save $1000 each month but the prices of his old 
car and of the new one decrease of 1.5 percent per month.
Furthermore this percent of loss increases of `0.5` percent 
at the end of every two months.
Our man finds it difficult to make all these calculations.

**Can you help him?**

How many months will it take him to save up enough money to buy the car he wants, and how much money will he have left over?

**Parameters and return of function:**
```
parameter (positive int or float, guaranteed) startPriceOld (Old car price)
parameter (positive int or float, guaranteed) startPriceNew (New car price)
parameter (positive int or float, guaranteed) savingperMonth 
parameter (positive float or int, guaranteed) percentLossByMonth

nbMonths(2000, 8000, 1000, 1.5) should return [6, 766] or (6, 766)
```
###  Detail of the above example:
```
end month 1: percentLoss 1.5 available -4910.0
end month 2: percentLoss 2.0 available -3791.7999...
end month 3: percentLoss 2.0 available -2675.964
end month 4: percentLoss 2.5 available -1534.06489...
end month 5: percentLoss 2.5 available -395.71327...
end month 6: percentLoss 3.0 available 766.158120825...
return [6, 766] or (6, 766)

```

where `6` is the number of months at **the end of which** he can buy the new car and `766` is the nearest integer to `766.158...` (rounding `766.158` gives `766`).

**Note:** 

Selling, buying and saving are normally done at end of month.
Calculations are processed at the end of each considered month
but if, by chance from the start, the value of the old car is bigger than the value of the new one or equal there is no saving to be made, no need to wait so he can at the beginning of the month buy the new car:
```
nbMonths(12000, 8000, 1000, 1.5) should return [0, 4000]
nbMonths(8000, 8000, 1000, 1.5) should return [0, 0]
```

We don't take care of a deposit of savings in a bank:-)

Answer: {"fn_name": "nbMonths", "inputs": [[2000, 8000, 1000, 1.5], [8000, 12000, 500, 1], [18000, 32000, 1500, 1.25], [7500, 32000, 300, 1.55]], "outputs": [[[6, 766]], [[8, 597]], [[8, 332]], [[25, 122]]]}
user: # Introduction 

Digital Cypher assigns to each letter of the alphabet unique number. For example:

```
 a  b  c  d  e  f  g  h  i  j  k  l  m
 1  2  3  4  5  6  7  8  9 10 11 12 13
 n  o  p  q  r  s  t  u  v  w  x  y  z
14 15 16 17 18 19 20 21 22 23 24 25 26
```

Instead of letters in encrypted word we write the corresponding number, eg. The word scout:

```
 s  c  o  u  t
19  3 15 21 20
```
Then we add to each obtained digit consecutive digits from the key. For example. In case of key equal to `1939` :

```
   s  c  o  u  t
  19  3 15 21 20
 + 1  9  3  9  1
 ---------------
  20 12 18 30 21
  
   m  a  s  t  e  r  p  i  e  c  e
  13  1 19 20  5 18 16  9  5  3  5
+  1  9  3  9  1  9  3  9  1  9  3
  --------------------------------
  14 10 22 29  6 27 19 18  6  12 8
```

# Task

Write a function that accepts `str` string and `key` number and returns an array of integers representing encoded `str`.

# Input / Output

The `str` input string consists of lowercase characters only.
The `key` input number is a positive integer.

# Example

```
Encode("scout",1939);  ==>  [ 20, 12, 18, 30, 21]
Encode("masterpiece",1939);  ==>  [ 14, 10, 22, 29, 6, 27, 19, 18, 6, 12, 8]
```

# Digital cypher series
- [Digital cypher vol 1](https://www.codewars.com/kata/592e830e043b99888600002d)
- [Digital cypher vol 2](https://www.codewars.com/kata/592edfda5be407b9640000b2)
- [Digital cypher vol 3 - missing key](https://www.codewars.com/kata/5930d8a4b8c2d9e11500002a)

Answer: {"fn_name": "encode", "inputs": [["scout", 1939], ["masterpiece", 1939]], "outputs": [[[20, 12, 18, 30, 21]], [[14, 10, 22, 29, 6, 27, 19, 18, 6, 12, 8]]]}
user: ##Task:

You have to write a function **pattern** which creates the following pattern upto n number of rows. *If the Argument is 0 or a Negative Integer then it should return "" i.e. empty string.*

##Pattern:

    (n)
    (n)(n-1)
    (n)(n-1)(n-2)
    ................
    .................
    (n)(n-1)(n-2)....4
    (n)(n-1)(n-2)....43
    (n)(n-1)(n-2)....432
    (n)(n-1)(n-2)....4321
    
##Examples:

pattern(4):

    4
    43
    432
    4321
    
pattern(6):
 
    6
    65
    654
    6543
    65432
    654321



```Note: There are no blank spaces```

```Hint: Use \n in string to jump to next line```

Answer: {"fn_name": "pattern", "inputs": [[1], [2], [5], [0], [-25]], "outputs": [["1"], ["2\n21"], ["5\n54\n543\n5432\n54321"], [""], [""]]}
user: Just another day in the world of Minecraft, Steve is working on his new project -- building a beacon pyramid in front of his house.

![Beacon pyramid](http://www.minecraft101.net/reference/images/beacon_pyramid_thb.jpg)

Steve has already obtained the beacon (the glass wrapped blue thingy on the top), he just needs to build the pyramid. Each level of the pyramid is built using one of the following four kinds of block: gold, diamond, emerald, and iron. Since these four kinds of blocks are relatively hard to collect, Steve needs to know exactly how many of each kind is required to build a pyramid of level N.

Assume that the top level of the pyramid uses gold blocks, the second level uses diamond blocks, the third level uses emerald blocks, the fourth level uses iron blocks, and the fifth level uses gold blocks, etc. (if you are a Minecraft player, you know it's not neccessary the right way to build the pyramid. Let's just assume it is for the sake of this kata ;-))

Implement a function that takes one argument which is the number of levels of the pyramid, and returns an object of the form: `{total: 9, gold: 9, diamond: 0, emerald: 0, iron: 0}`.

---

To all the Minecraft players out there: 
feel free to expand this series or let me know if you have any ideas related to Minecraft that can be turned into codewars puzzles. Some ideas I have that might potentially be turned into katas:

* distance traveled in real world vs. in Nether
* shortest path problems related to mining diamonds/gold/goodies that appears in different levels under ground
* growth of animal population from breeding
* redstone stuff?!

If you do end up expanding this series, please send me a link of your kata so I can check it out and include a link to your kata here :-)

* [Minecraft Series #2: Minimum amount of fuel needed to get some iron ingots](https://www.codewars.com/kata/minecraft-series-number-2-minimum-amount-of-fuel-needed-to-get-some-iron-ingots/ruby)
* [Minecraft Series #3: Lava is amazing! ](https://www.codewars.com/kata/583a23d40cf946ec380002c2)
* [Minecraft Series #4: Lava is amazing, however...](https://www.codewars.com/kata/583a6b0b171f3a3c3f0003e3)

Answer: {"fn_name": "blocks_to_collect", "inputs": [[1], [2], [3]], "outputs": [[{"total": 9, "gold": 9, "diamond": 0, "emerald": 0, "iron": 0}], [{"total": 34, "gold": 9, "diamond": 25, "emerald": 0, "iron": 0}], [{"total": 83, "gold": 9, "diamond": 25, "emerald": 49, "iron": 0}]]}
user: You have stumbled across the divine pleasure that is owning a dog and a garden. Now time to pick up all the cr@p! :D

Given a 2D array to represent your garden, you must find and collect all of the dog cr@p - represented by '@'.

You will also be given the number of bags you have access to (bags), and the capactity of a bag (cap). If there are no bags then you can't pick anything up, so you can ignore cap.

You need to find out if you have enough capacity to collect all the cr@p and make your garden clean again. 

If you do, return 'Clean', else return 'Cr@p'.

Watch out though - if your dog is out there ('D'), he gets very touchy about being watched. If he is there you need to return 'Dog!!'.

For example:

x=
[[\_,\_,\_,\_,\_,\_]
 [\_,\_,\_,\_,@,\_]
 [@,\_,\_,\_,\_,\_]]

bags = 2, cap = 2

return  --> 'Clean'

Answer: {"fn_name": "crap", "inputs": [[[["_", "_", "_", "_"], ["_", "_", "_", "@"], ["_", "_", "@", "_"]], 2, 2], [[["_", "_", "_", "_"], ["_", "_", "_", "@"], ["_", "_", "@", "_"]], 1, 1], [[["_", "_"], ["_", "@"], ["D", "_"]], 2, 2], [[["_", "_", "_", "_"], ["_", "_", "_", "_"], ["_", "_", "_", "_"]], 2, 2], [[["@", "@"], ["@", "@"], ["@", "@"]], 3, 2]], "outputs": [["Clean"], ["Cr@p"], ["Dog!!"], ["Clean"], ["Clean"]]}
user: Your dad doesn't really *get* punctuation, and he's always putting extra commas in when he posts. You can tolerate the run-on sentences, as he does actually talk like that, but those extra commas have to go!

Write a function called ```dadFilter``` that takes a string as argument and returns a string with the extraneous commas removed. The returned string should not end with a comma or any trailing whitespace.

Answer: {"fn_name": "dad_filter", "inputs": [["all this,,,, used to be trees,,,,,,"], ["Listen,,,, kid,,,,,,"], ["Luke,,,,,,,,, I am your father,,,,,,,,,  "], ["i,, don't believe this round earth,,, show me evadence!!"], ["Dead or alive,,,, you're coming with me,,,   "]], "outputs": [["all this, used to be trees"], ["Listen, kid"], ["Luke, I am your father"], ["i, don't believe this round earth, show me evadence!!"], ["Dead or alive, you're coming with me"]]}
user: Write a program to determine if two numbers are coprime. A pair of numbers are coprime if their greatest shared factor is 1. For example:
```
20 and 27
Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 27: 1, 3, 9, 27
Greatest shared factor: 1
20 and 27 are coprime```
An example of two numbers that are not coprime:
```
12 and 39
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 39: 1, 3, 13, 39
Greatest shared factor: 3
12 and 39 are not coprime```
If the two inputs are coprime, your program should return true. If they are not coprime, your program should return false.

The inputs will always be two positive integers between 2 and 99.

Answer: {"fn_name": "are_coprime", "inputs": [[20, 27], [12, 39], [17, 34], [34, 17], [35, 10], [64, 27]], "outputs": [[true], [false], [false], [false], [false], [true]]}
user: Jack really likes his number five: the trick here is that you have to multiply each number by 5 raised to the number of digits of each numbers, so, for example:
```python
multiply(3)==15
multiply(10)==250
multiply(200)==25000
multiply(0)==0
multiply(-3)==-15
```

Answer: {"fn_name": "multiply", "inputs": [[10], [5], [200], [0], [-2]], "outputs": [[250], [25], [25000], [0], [-10]]}
user: ## Task
Given an array of strings, reverse them and their order in such way that their length stays the same as the length of the original inputs.

### Example:

```
Input:  {"I", "like", "big", "butts", "and", "I", "cannot", "lie!"}
Output: {"!", "eilt", "onn", "acIdn", "ast", "t", "ubgibe", "kilI"}
```

Good luck!

Answer: {"fn_name": "reverse", "inputs": [[["I", "like", "big", "butts", "and", "I", "cannot", "lie!"]], [["?kn", "ipnr", "utotst", "ra", "tsn", "iksr", "uo", "yer", "ofebta", "eote", "vahu", "oyodpm", "ir", "hsyn", "amwoH"]]], "outputs": [[["!", "eilt", "onn", "acIdn", "ast", "t", "ubgibe", "kilI"]], [["How", "many", "shrimp", "do", "you", "have", "to", "eat", "before", "your", "skin", "starts", "to", "turn", "pink?"]]]}
user: I'm afraid you're in a rather unfortunate situation. You've injured your leg, and are unable to walk, and a number of zombies are shuffling towards you, intent on eating your brains. Luckily, you're a crack shot, and have your trusty rifle to hand.

The zombies start at `range` metres, and move at 0.5 metres per second. Each second, you first shoot one zombie, and then the remaining zombies shamble forwards another 0.5 metres.

If any zombies manage to get to 0 metres, you get eaten. If you run out of ammo before shooting all the zombies, you'll also get eaten. To keep things simple, we can ignore any time spent reloading.

Write a function that accepts the total number of zombies, a range in metres, and the number of bullets you have.

If you shoot all the zombies, return "You shot all X zombies."
If you get eaten before killing all the zombies, and before running out of ammo, return "You shot X zombies before being eaten: overwhelmed."
If you run out of ammo before shooting all the zombies, return "You shot X zombies before being eaten: ran out of ammo."

(If you run out of ammo at the same time as the remaining zombies reach you, return "You shot X zombies before being eaten: overwhelmed.".)

Good luck! (I think you're going to need it.)

Answer: {"fn_name": "zombie_shootout", "inputs": [[3, 10, 10], [100, 8, 200], [50, 10, 8], [10, 10, 10], [17, 8, 200], [9, 10, 8], [20, 10, 20], [100, 49, 200], [50, 10, 19], [50, 10, 49], [100, 10, 20], [19, 10, 20], [20, 10, 100], [20, 10, 19], [19, 15, 19], [19, 3, 19]], "outputs": [["You shot all 3 zombies."], ["You shot 16 zombies before being eaten: overwhelmed."], ["You shot 8 zombies before being eaten: ran out of ammo."], ["You shot all 10 zombies."], ["You shot 16 zombies before being eaten: overwhelmed."], ["You shot 8 zombies before being eaten: ran out of ammo."], ["You shot all 20 zombies."], ["You shot 98 zombies before being eaten: overwhelmed."], ["You shot 19 zombies before being eaten: ran out of ammo."], ["You shot 20 zombies before being eaten: overwhelmed."], ["You shot 20 zombies before being eaten: overwhelmed."], ["You shot all 19 zombies."], ["You shot all 20 zombies."], ["You shot 19 zombies before being eaten: ran out of ammo."], ["You shot all 19 zombies."], ["You shot 6 zombies before being eaten: overwhelmed."]]}
user: # Introduction

There is a war and nobody knows - the alphabet war!  
There are two groups of hostile letters. The tension between left side letters and right side letters was too high and the war began.

# Task

Write a function that accepts `fight` string consists of only small letters and return who wins the fight. When the left side wins return `Left side wins!`, when the right side wins return `Right side wins!`, in other case return `Let's fight again!`.

The left side letters and their power:
```
 w - 4
 p - 3
 b - 2
 s - 1
```
The right side letters and their power:
```
 m - 4
 q - 3
 d - 2
 z - 1
```
The other letters don't have power and are only victims.

# Example

# Alphabet war Collection



Alphavet war 


Alphabet war - airstrike - letters massacre


Alphabet wars - reinforces massacre


Alphabet wars - nuclear strike


Alphabet war - Wo lo loooooo priests join the war

Answer: {"fn_name": "alphabet_war", "inputs": [["z"], ["zdqmwpbs"], ["wq"], ["zzzzs"], ["wwwwww"]], "outputs": [["Right side wins!"], ["Let's fight again!"], ["Left side wins!"], ["Right side wins!"], ["Left side wins!"]]}
user: #### Task:

Your job here is to implement a function `factors`, which takes a number `n`, and outputs an array of arrays comprised of two
parts, `sq` and `cb`. The part `sq` will contain all the numbers that, when squared, yield a number which is a factor of `n`,
while the `cb` part will contain all the numbers that, when cubed, yield a number which is a factor of `n`.  Discard all `1`s
from both arrays.

Both `sq` and `cb` should be sorted in ascending order.

#### What it looks like:

```python
factors(int) #=> [
  sq (all the numbers that can be squared to give a factor of n) : list,
  cb (all the numbers that can be cubed   to give a factor of n) : list
]
```

#### Some examples:

Also check out my other creations — [Keep the Order](https://www.codewars.com/kata/keep-the-order), [Naming Files](https://www.codewars.com/kata/naming-files), [Elections: Weighted Average](https://www.codewars.com/kata/elections-weighted-average), [Identify Case](https://www.codewars.com/kata/identify-case), [Split Without Loss](https://www.codewars.com/kata/split-without-loss), [Adding Fractions](https://www.codewars.com/kata/adding-fractions),
[Random Integers](https://www.codewars.com/kata/random-integers), [Implement String#transpose](https://www.codewars.com/kata/implement-string-number-transpose), [Implement Array#transpose!](https://www.codewars.com/kata/implement-array-number-transpose), [Arrays and Procs #1](https://www.codewars.com/kata/arrays-and-procs-number-1), and [Arrays and Procs #2](https://www.codewars.com/kata/arrays-and-procs-number-2).

If you notice any issues or have any suggestions/comments whatsoever, please don't hesitate to mark an issue or just comment. Thanks!

Answer: {"fn_name": "factors", "inputs": [[1], [4], [16], [81], [80], [100], [5], [120], [18], [8]], "outputs": [[[[], []]], [[[2], []]], [[[2, 4], [2]]], [[[3, 9], [3]]], [[[2, 4], [2]]], [[[2, 5, 10], []]], [[[], []]], [[[2], [2]]], [[[3], []]], [[[2], [2]]]]}
user: # Summation

Write a program that finds the summation of every number from 1 to num. The number will always be a positive integer greater than 0.

For example:
```if-not:racket
~~~
summation(2) -> 3
1 + 2

summation(8) -> 36
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8
~~~
```
```if:racket
~~~racket
(summation 2) ; 3  (+ 1 2)
(summation 8) ; 36 (+ 1 2 3 4 5 6 7 8)
~~~
```

Answer: {"fn_name": "summation", "inputs": [[1], [8], [22], [100], [213]], "outputs": [[1], [36], [253], [5050], [22791]]}
user: Consider having a cow that gives a child every year from her fourth year of life on and all her subsequent children do the same.

After n years how many cows will you have?
Return null if n is not an integer.

Note: Assume all the cows are alive after n years.

Answer: {"fn_name": "count_cows", "inputs": [[1], [3], [5]], "outputs": [[1], [2], [4]]}