"Whoever" is correct. "Who" asks the question to an answer with "He / She". Q: Who did that? A: She / He did that. "Whom" asks the question to an answer with "Him / Her". Q: For whom did I do this? H: For him / her. "Whom" is always the object of the sentence. The subject always executes an action on the subject, for example: John cooked chicken for Karen. For whom did John cook chicken? Possible answers: For Karen. For her.

"whom" and "whomever" are only necessary when the pronoun is used as an object of a verb, and even for that people tend to prefer "who" and "whoever" nowadays. ex) I thank whomever it was that created this. (object of "thank"). (Most people say "I thank whoever..." for this) In your sentence, it only serves as a subject, so there is absolutely no reason why "whomever" has to enter into the picture. It should be "Whoever".

It's definitely "whoever", because that's the subject of the sentence. "Whoever created this problem should be responsible for solving it." (pattern: responsible for [verb]ing)