Questions without winning criterion should be closed early (as 'not constructive', better, if possible, with an own category: Missing winning criterion.
Else, people start working on CG-solutions, and emphasize the charcter count. Soon everybody follows and threats it as a golf question. They vote each other up, and nobody can stop it anymore.
Closing the question later is too late. The first answers more votes. I guess many people revisit a question rarely after publishing their own solution - except, if they earn much upvotes.
Vote to close, and leave a comment that you did so, and explain why. A closed question can be reopened, if the winning criterion is added later, but it avoids answers.
We need more discipline in handling the rules. I like CG-questions too, but I don't like to pretend that I did not see the missing criterion, nor do I like to produce the de facto pressure, which exists, after 2 or 3 answers where submitted with "48 chars" or "55 chars" in the headline.
I guess this is the better way to handle questions without winning criteria than handling the answers as discussed here, which would be the way to handle it late.