In Three Men in a Boat, Harris walks into the maze at Hampton Court saying you only have to “keep on taking the first turning to the right”. One of you draws a maze. The other says whether Harris’s rule would reach the middle. Then build it here, guess, and watch two searchers try it: Harris’s rule, and a careful search that always finds the shortest way if there is one.
It starts as the island trap. Tap a square to plant a hedge or clear it. The entrance is at the bottom (▲) and the middle is marked ◆. Arrow keys move; Enter or Space plants.
Will “keep taking the first turning to the right” reach the middle?
where Harris’s rule went · the shortest way
A child builds places in WorldForge on Spark & Anvil. Send your maze to WorldForge as a short piece of text, copied and pasted by hand, and your child can walk Beam through it. A place your child builds there comes back the same way: they press “Copy for the Hedge Maze”, and you paste it below. Nothing is sent anywhere.
The hedge maze at Hampton Court Palace was planted around 1690. In Jerome K. Jerome’s comic novel Three Men in a Boat (1889, chapter 6), Harris leads a crowd in with his rule. They are soon lost, and so is the young keeper who comes to help.
Keeping one hand on the hedge always gets you there when two things are true: the paths are one square wide, and every hedge is joined, through other hedges, to the outside edge. Then the hand is tracing one long hedge, and it passes every path. It fails when a block of hedge stands on its own, an island: the hand goes round the island’s outside and walks straight past the opening on its inner side. (In an open field it fails too: the hand never leaves the edge.) A breadth-first search, which looks one step out, then two, then three, never misses a way that is there. Edward Moore described it for mazes in 1959.
Sources: J. K. Jerome, Three Men in a Boat (1889); E. F. Moore, “The shortest path through a maze” (1959). The children’s side is WorldForge on Spark & Anvil, where Beam the woodpecker runs the same two searches.