"one or other": correct or incorrect?

Solution 1:

It's grammatical and is often used when the writer or speaker isn't sure about the identity of two or more alternatives. He saw one or other of the men means that he certainly saw a man, but didn't know which one.

Solution 2:

In the pattern ~ of the [noun], ~ cannot be filled by an adjective, which is what other is usually considered to be. It is most common for that slot to be filled by a determiner. There are examples of adjectives becoming reanalyzed as determiners (e.g., several), so this suggests that, for this author, other is a determiner. Examples outside the particular string one or other of the are attested but rare.