Arrange the following words according to standard dictionary rules: "Man", "Men", "Machine", "Method", "Methodical", "Make", "Mentor", "Map". Which of them will be at the end?

Let us sort all the given words alphabetically:
1. All words start with 'M'. Look at the second letter: 'a' and 'e'.
2. Group with 'a': Machine, Make, Man, Map.
3. Group with 'e': Men, Mentor, Method, Methodical.

Let us sort the 'e' group to find the last word:

* Compare the third letters of Men, Mentor, Method, Methodical:
* Men ('n')
* Mentor ('n')
* Method ('t')
* Methodical ('t')

* Between the 'n' sub-group and 't' sub-group, the 't' sub-group comes later alphabetically.
* Now compare Method and Methodical:
* Both start with the exact same prefix "Method".
* "Methodical" has additional letters following the prefix, so it appears after "Method" in the dictionary.

Thus, "Methodical" will be at the very end.