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Despite that, they don't have a lot of power. They do damage, but not much. That and you have to consider types and such. Imagine trying to kill a steel type with nothing but HMs. Especially a Steelix in the E4, where the CPU is far more aggressive in it's play.
I've tested that before, pushing an HM slave through the E4, and it's almost impossible to do. The point of my challenge was to be challenging, but not next-to-impossible. (because my idea isn't just for challenge masters, it's meant to be doable by anyone...even a complete Pokemon Challenge novice.)
But yeah. Limited type selection and a very limited choice of moves, depending on which pokemon you choose would make it quite difficult to battle against types with resistance to the HM types. You'd be stalled for hours. Personally I think a challenge is a waste of time if it can't be completed in less than 20 hours...I guarantee you it'd take longer than 20 hours if you were only allowed to use HM moves in battle, because of the insane amount of grinding you'd have to do in order to beat the Gym Leaders and E4, not to mention the canon storyline battles with the Rival, and Evil Team(s) of the version.
Additionally there are only 6 rules overall to my challenge, but I spent time to flesh the rules out to explain what to do in different situations.