Picard would win the no-win scenario. How? By making it so.
Garak would lose the scenario and in disgrace drop out of the academy. Not till years later, running into him on Tzenketh where he was working as a cobbler, would you find out that in fact the dropping out was a cover. He had been tapped by one of the intelligence agencies after he'd revenged himself on the Kobayashi Maru test givers.
Harry Kim was slapped in the face by his teacher on the way though the door. Not since Jonathan Archer...oh never mind...I'm an asshole.