24 people are at a rowing meet.
They have 4 boats, each fitting exactly 6 people.
Over several days,
all the participants are assigned to boats,
with assignments possibly changing daily.

You're responsible for allocating the members into boats,
with the goal of ensuring that each of the
${24 \choose 2} = 276$ unique pairs of participants
shares a boat on at least one day.

What's the minimum number of days the rowing meet
must last for this to be possible?

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Solve the problem and document your journey in an index.md file explaining your solution.

If you want to include code or external files in your index.md, feel free to include them inline or link to separate files via markdown.
You are allowed to use multiple files.
Describe your different methods to reach the solution even ones that did not bear fruits.

Keep the final product readable.
Make it complete but focus the attention on the most important things.

You are allowed to use KaTeX formatting via $ and $$.
You are allowed to write and run code.
If you explicitly create a construction, format it in as a JSON array, where each element is an array of four arrays containing 6 integers, 0-indexed.