Maze

How to escape any maze

The oldest reliable trick is the wall follower, or the hand-on-the-wall rule. Pick one hand, say your right, and imagine keeping it pressed to the wall as you move. At every junction you turn as far that way as you can, and at a dead end you turn around, still tracing the same wall. Keep to the same hand for the whole run and the wall leads you around every dead-end pocket and out through the exit. Mazes generated fresh like these are almost always perfect mazes, meaning no loops and exactly one path between any two points, and that is precisely the condition that makes wall-following certain to work. On a small grid you can often beat the arrows entirely by planning; on a big one, the hand rule is your safety net when the plan runs out.

Faster route-finding tips

Wall-following guarantees an escape but not a quick one, since it can march you down every blind alley. When you can see more of the layout, plan with your eyes and use the keys only to carry out the plan.

• Commit to one hand for the entire maze; switching halfway can leave you circling a section forever.
• When the exit is in sight, drop the wall rule and head straight for it through the open corridors.
• At a junction, glance down each branch for a visible dead end before you commit to one.
• Mind the far corners. Generators love tucking long dead ends there, so treat a corner corridor with suspicion unless the exit sits in it.
• If you must backtrack, retrace decisively instead of dithering in the same corridor.
• Speed comes from reading a few cells ahead, not from mashing the direction keys.

Two methods with names attached

The wall follower has smarter cousins. In the 1800s a French engineer named Charles Tremaux worked out a marking method that beats any maze, loops included. Each time you walk a corridor, mark it once at the entrance. At a junction, prefer a corridor with no marks, and never enter one that already carries two. Follow those rules and you will reach the exit, and your marks will show a clean route back. The other workhorse is dead-end filling, which suits mazes you can see from above, like these. Find every dead end and mentally wall it off back to its junction. Repeat, because filling one blind alley often turns the corridor feeding it into a new dead end. What survives the filling is the true path, and often the whole solution simply appears. Neither method needs luck. That is the quiet truth of mazes: they fall to patience and bookkeeping, never to speed alone.

Labyrinths and myth

The maze is one of humanity's oldest ideas. Greek myth tells of the Labyrinth built by the craftsman Daedalus at Knossos on Crete to hold the Minotaur. The hero Theseus survived it only by unspooling a thread from Ariadne so he could find his way back out, and that thread even shaped our language: a ball of thread was once called a clew, which is where the word clue comes from. Medieval cathedrals kept the older form alive, laying unicursal labyrinths into their floors as walking paths for prayer; the famous one at Chartres in France was set around 1200. Strictly, that classical labyrinth was unicursal, a single winding path with no choices. A true maze, like the ones here, is multicursal, full of branches and dead ends built to mislead. The most famous survivor is the hedge maze at Hampton Court Palace, planted around 1700 and still swallowing tourists today, while the yew maze at Longleat, planted in 1975, packs nearly two miles of paths into a single English garden.

Mazes for robots

Maze solving became an engineering sport, too. Since the late 1970s, micromouse contests have set small robot mice loose in a sixteen-by-sixteen walled maze. Each robot explores first, builds a map, then computes the best route and sprints it, and the top machines cross the maze in a handful of seconds. Their classic method, flood fill, scores every cell by its distance from the goal and always moves downhill. It is the same family of thinking as dead-end filling, and the lesson transfers straight back to the human game: explore first, learn the shape, then run your fastest line.