Question 1208378
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How many 7-digit numbers can be formed using the digits 1, 2, 3, 4, and 5, 
provided that any two distinct digits in this number are consecutive?
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The formulation of the problem is murky and unclear.


Looking at this problem, I see that a person who created it (math composer) 
has no necessary skills to make this post as correct, clear, accurate,
interesting and meaningful mathematical problem.


I also do not see an attractive mathematical idea behind it.


Therefore, I prefer do not touch it and do not participate.


Had it be differently, I would (probably) think differently.



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Edwin, to your post as @mccravyedwin, you may have your own view and opinion, 
and I may have my own view and opinion, and they not necessary should be the same.
I respect your opinion and do not impose my opinion.



Regarding their writing, in our days, any Internet browser has a built-in translator,
which provides perfect (or almost perfect) translation.


So, if their wording was not perfect, it was only because they did not work on it, and it was their fault.


To guess the thoughts in their head is not my task and is not my specialty/desire/function here.


If they can not formulate perfectly and accurately, it means that they can not think accurately;
in turn, it means that they are not ready to understand the solutions (and even formulations) 
of such problems, at all.


One wise man said once that if people can nor speak English clearly, 
it is often because they can not speak clearly in their native language.