Numbered Triangles
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Our robots like games that require the ability to calculate equations. Mission control recently sent them the new game to occupy their time while flying from one Island to the next. This game is called "Numbered Triangles". Players take 6 chips from the pile, each chip is made of an equilateral triangle with three numbers one on each edge. You can move, rotate and flip the chips so they form a hexagon. The hexagon is only legal if the adjacent edges for each triangle have matching numbers.

The score for a legal hexagon is the sum of the numbers on the outside six edges. The player's goal is to find the highest score that can be achieved with the given six chips.

Each chip is represented as a list with three positive numbers. You should help the robots find the highest score for the given chips and return the score as a number. If you cannot form legal hexagon from the chips, then return a score of 0.

Input: The chip info as a list of lists. Each list contain three integers.

Output: The highest possible score as an integer.

Example:

checkio([[1, 4, 20], [3, 1, 5], [50, 2, 3],
[5, 2, 7], [7, 5, 20], [4, 7, 50]]) == 152
checkio([[1, 10, 2], [2, 20, 3], [3, 30, 4],
[4, 40, 5], [5, 50, 6], [6, 60, 1]]) == 210
checkio([[1, 2, 3], [2, 1, 3], [4, 5, 6],
[6, 5, 4], [5, 1, 2], [6, 4, 3]]) == 21
checkio([[5, 9, 5], [9, 6, 9], [6, 7, 6],
[7, 8, 7], [8, 1, 8], [1, 2, 1]]) == 0

How it is used: This concept is used in optimization systems; you have constraints but you should work to get the most with these constraints. Of course this algorithm can be useful for the realisation of gameplay mechanics.

Precondition:
len(chips) == 6
all(all(0 < x < 100 for x in ch) for ch in chips)

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Code:
Other:
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.