13 itself is an odd number.

Thank you so much for explaining this! Your comment is super helpful.

However, the statement 'A positive integer can be represented as a sum of consecutive integers if and only if it is divisible by an odd number' is not always true:
13 is a sum of consecutive integers (6+7) and is not divisible by an odd number (this seems to apply to any prime number > 2 if fact)

cool solution except one caveat here:

assertEquals("elppa ", Kata.reverseWords("apple "));

=> fails because trailing spaces are removed