Consider that you take steps that are 1/4 the length of the room.
In two steps you've reached the halfway mark... so far tracking with Zeno.
In three steps you've reached half of what was left in two steps... Zeno is feeling awefully smug!
In four steps you've reached the destination... Zeno is quite confused at this point.

The easier resolution lies in realizing that just because you cross 1/2 the distance you are not restricted to only that or put another way the discreteness of steps resolves the paradox.

By this I mean that Zeno's paradox is completely true: if you took a step that was EACH TIME half the distance to the end of the room, (in other words if you shortened your step each time) you would never reach it (or rather asymptotically reach it which means it will take an infinte amount of time to cover the final infinitely small distance).


But this doesn't mean that ALL movement is impossible. When the paradox states that you have to move half the distance, that is true... but at the point where you reach the 1/2 way mark you don't stop... you actually go further than half way. So if you take steps that are a third the distance to the end, after the first step you have covered the 1/2 way mark (Zeno Smiles), after the second step you have covered half the remaining distance (Zeno Laughs), but after the third step you are at the end (Zeno Crys).


So the paradox is no paradox at all: if you follow it exactly, shortening your step by half, then it's true; if you take same sized steps the whole time, then it isn't.