Two people a mile apart from each other work out the following plan for meeting each other. One person starts by walking half the distance between them. Then the second person walks half the new distance between them. They keep alternating like this. At what point along the road will they meet?

From the symmetry of the problem, it is tempting to say that they each walk the same distance, but this is obviously incorrect, since the first person starts off by walking half the total distance.

No algebra is required. If you look at the problem the right way, the answer should leap out at you.