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How to solve this problem in the fastest way possible?

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    Welcome to MSE. You'll get a lot more help if you show that you have made a real effort to solve the problem yourself, even if you haven't made much progress. What are your thoughts? What have you tried? How far could you get? Where are you stuck? This question will likely be closed if you don't add more context. Please respond by editing the question body. Clarifications don't belong in the comments. – saulspatz Jul 20 '21 at 15:48
  • Although some may question posting a puzzle on mathSE, personally, I think the question about how to analytically attack this problem does (at least potentially) relate to math. Per the comment of @saulspatz, please see this article re protocol on mathSE questions. Also, to repeat, your work/analysis belongs in the (edited) question itself, not in the comments. – user2661923 Jul 20 '21 at 15:52
  • For convenience to reviewers, I edited your question to embed the diagram directly into the question. In general, see this article for options of embedding a diagram. Note also, my (unusual) <img src="https://i.stack.imgur.com/7pPTY.png" width="600"> method of enlarging the diagram. – user2661923 Jul 20 '21 at 15:57
  • The spoiler is that you can do it in $6$, but it is not obvious. – Vepir Jul 20 '21 at 17:08
  • Think outside the box. Literally – Mark Jul 21 '21 at 22:25

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