The riddle
How Far Can a Dog Run Into the Woods?
Halfway in, then on the way out
Picture a straight path through woods that are two miles across. At the entrance the dog is at distance 0, and each step takes it one step deeper. After one mile it is as far from the nearest edge as it will ever be. Every step past that moves it closer to the far edge, so it is running out of the woods. Halfway is the deepest point. On a path four miles across that point is two miles in, and on a path half a mile across it is a quarter of a mile in.
Into and out of
Wiktionary defines halfway as half of the way between two points, midway. The riddle plays on the pair into and out of. A listener pictures the dog heading farther and farther in and never thinks of the far side. The riddle works because the woods have two edges and the question mentions only one.
Other animals, same answer
The question is also told about a fox, a rabbit or a squirrel instead of a dog, and the answer is halfway for each. A few people answer the question literally and say the distance depends on the animal and the woods, which is a fair thing to say about real dogs. The riddle is not about the animal. It is about where a path through woods turns from in to out.
Drawing it on paper
Draw a line for the path, mark both ends as edges and put a dot in the middle. Ask the group how far from an edge the dog is at the dot, and what happens to that distance with each step beyond it. Another riddle with a plain-sounding question is where does one wall meet the other wall.