He's furious when the Cabbie is killed and he's denied the answer to the puzzle.

My thought was - Sherlock didn't take his pill. (Neither did the cabbie, but it might've been dropped and lost when he was shot, whereas Sherlock should've still had his.) That means they could've tested it in a lab to see if it contained the poison or not. (I would think they'd want to do that anyway, as evidence.) So Sherlock could've easily gotten his answer, even though the cabbie was dead.

Does this mean I'm smarter than Sherlock Holmes? :)