SergO_33
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Attached are the clearly stated conditions of the problem, which, in this form, I think, already provide a good hint. It can be solved not only by a non-systematic trial-and-error method, I assure you.
Nelyo, thank you for formulating the problem so clearly! )) Everything is so well organized that I couldn't resist (I was just too lazy to solve it) and wrote a program to iterate through the possible solutions, and now I can confidently state: the minimum number of steps to solve the problem is 6! Moreover, the order in which you approach the "correct" monks does not matter.
