# Saw the Stick

An enormous puppy was looking down at her with large round eyes, and feebly stretching out one paw, trying to touch her. "Poor little thing!" said Alice, in a coaxing tone, and she tried hard to whistle to it; but she was terribly frightened all the time at the thought that it might be hungry, in which case it would be very likely to eat her up in spite of all her coaxing.

Hardly knowing what she did, she picked up a little bit of stick, and held it out to the puppy; whereupon the puppy jumped into the air off all its feet at once, with a yelp of delight, and rushed at the stick, and made believe to worry it; then Alice dodged...

"Puzzles from Wonderland." Lewis Carroll

The robots want to saw the stick in several pieces. The length of the stick is N inches. We should help our robots saw the stick. All of the parts should have integer lengths (1, 2, 3 .. inches, but not 1.2). As we love the numerical series and especially the Triangular numbers ( read more about Triangular numbers on Wikipedia ), you should saw the stick so that the lengths form the consecutive fragment of the Triangular numbers series with the maximum quantity (fragment's length). The parts should have different lengths (no repeating). For example: 64 should divided at 15, 21, 28 , because 28, 36 is shorter and 1, 3, 15, 45 is not a consecutive fragment.

You are given a length of the stick (N). You should return the list of lengths (integers) for the parts in ascending order. If it's not possible and the problem does not have a solution, then you should return an empty list.

Input: A length of the stick as an integer.

Output: A fragment of the Triangular numbers as a list of integers (sorted in ascending order) or an empty list.

Example:

```checkio(64) == [15, 21, 28]
checkio(371) == [36, 45, 55, 66, 78, 91]
checkio(225) == [105, 120]
checkio(882) == []
```

How it is used: In this task you will learn about triangular numbers. A triangular number or triangle number counts the objects that form an equilateral triangle. This is an interesting sequence which has various applications.
Here’s a real world application: In a competitive tournament format that uses a round-robin group stages, the number of matches that need to be played between n teams is equal to the triangular number T n−1 . For example, a group stage with 4 teams requires 6 matches, and a group stage with 8 teams requires 28 matches.

Precondition: 0 < length < 1000

You should be an authorized user in order to see the full description and start solving this mission.
45
Settings
Code:
Other:
Invalid hot key. Each hot key should be unique and valid
Hot keys:
•  to Run Code: to Check Solution: to Stop:
CheckiO Extensions

CheckiO Extensions allow you to use local files to solve missions. More info in a blog post.

In order to install CheckiO client you'll need installed Python (version at least 3.8)

Install CheckiO Client first:

`pip3 install checkio_client`

`checkio --domain=py config --key=`

Sync solutions into your local folder

`checkio sync`

(in beta testing) Launch local server so your browser can use it and sync solution between local file end extension on the fly. (doesn't work for safari)

`checkio serv -d`

Alternatevly, you can install Chrome extension or FF addon

`checkio install-plugin`
`checkio install-plugin --ff`
`checkio install-plugin --chromium`

Read more here about other functionality that the checkio client provides. Feel free to submit an issue in case of any difficulties.

Pair Programming (Beta-version)

Welcome to Pair Programming! Engage in real-time collaboration on coding projects by starting a session and sharing the provided unique URL with friends or colleagues. This feature is perfect for joint project development, debugging, or learning new skills together. Simply click 'Start Session' to begin your collaborative coding journey!

Waiting for Pair Programming to start...

You are trying to join a pair programming session that has not started yet.

Please wait for the session creator to join.

Waiting for Pair Programming to reconnect...

It looks like the creator of the pair programming session closed the editor window.

It might happen accidentally, so that you can wait for reconnection.