# Bogglers

By Scott Kim|Monday, September 01, 2003

A-maze-ments
From spiritual quests to computer games, the ancient labyrinth enjoys renewed popularity worldwide. Wind your way through these novel offerings from modern mazemakers

Bath Path

Designer Adrian Fisher (www.mazemaker.com) has created hundreds of beautiful and innovative walk-through mazes all over the world, including, in 1993, the first Maize Maze, cut into acres of Pennsylvania cornfield. While traditional walk-through mazes use hedges as walls, many of Fisher's mazes rely instead on decoratively paved paths. In Bath, England, in 1984, Fisher created one such maze as part of the city's annual arts festival. The 7,000-square-foot elliptical maze (below, left) is made up of a stone path set in grass, with benches around the perimeter. At the center lies an Italian marble mosaic (below, right) that is 15 feet in diameter, representing the Gorgon's Head of Bath, a Roman sculpture uncovered in the 18th century.

Referring to the diagram of the maze that appears above, can you solve the following five challenges? In honor of the Roman spa that gave Bath its name, this diagram includes 14 hot-water taps (represented by faucet handles), and we've added six red paths. Unless the problem specifically refers to the taps or the paths, you can ignore them; they don't block the way.

1. [Easy] Can you find your way from the starting point at the bottom of the maze to the center? (This is much easier to solve on paper than in person.)

2. [Hard] Find the shortest possible route to the center of the maze.

3. [Hard] Find the longest possible path to the center that does not pass through any point twice.

4. [Hard] Find a solution that includes all six red paths and does not pass through any point twice.

5. [Hardest] Find a path to the center that passes through as few of the hot-water taps as possible. Hint: You should pass through fewer than five.

Tilt Maze Andrea Gilbert (www.clickmazes.com) is a leading inventor of computer-based maze puzzles. Her plank puzzles were recently released in hands-on form under the name River Crossing, by Binary Arts. An example of a tilt maze, one of her earliest innovations, is shown here. The challenge is to imagine tilting the board to get the ball into one of the three goal squares marked A, B, or C. On each move the ball rolls straight up, left, down, or right until it hits a wall and stops. The dotted line shows three possible consecutive moves.

1. [Easy] Roll the ball to reach goal A. Hint: To get started, use the three moves shown by the dotted line, then move up one square.

2. [Hard] Put the ball back in the upper left corner and roll the ball to reach goal B. The shortest solution takes nine moves.

3. [Hard] Put the ball back in the upper left corner and roll the ball to reach goal C. The shortest solution takes seven moves.

4. [Hardest] Put the ball back in the upper left corner and roll the ball to reach all three goals in succession in one path. You may visit the goals in any order. There is only one correct order.

Quizzical Quilt
Robert Abbott (www.logicmazes.com), inventor of the inductive-reasoning card game Eleusis, is a premier designer of multistate mazes, in which your next possible move depends not just on where you are but how you got there. Abbott's creations, which he describes as "mazes with rules," frequently employ arrows, numbers, or shapes that jump solvers from square to square, like a queen moving around a chessboard. Here is a maze Abbott designed for his sister Margie Ellis, inspired by her interest in quilt making.

1. [Easy] Start at the yellow flower at the bottom and jump from hexagon to hexagon until you reach the blue fish at the top. On each move you may travel any distance along a row of hexagons in the directions shown by the arrows, but the hexagon where you end a move must have either the same pattern or the same color as the hexagon at which you began. For instance, the gray line shows two possible consecutive moves: Starting at the yellow flower, move north two hexagons to the green flower. Then from the green flower, you move northeast to the green fish. Can you reach the blue fish in just five moves? There is more than one solution.

2. [Hard] Now add a new rule: You may not land on or travel over the black hexagon in the middle. Can you solve the maze in six moves?

3. [Harder] Start from the yellow flower just above the center and get to the blue fish at the top with no U-turns (in other words, after you land on a hexagon, you may not turn 180 degrees and move back in the opposite direction). All the previous rules still apply. The solution requires 10 moves.

4. [Hardest] Start from the yellow flower at the bottom and work your way to the blue fish at the top, making no U-turns. Hint: The solution to puzzle 3 is part of this solution, and you must retrace part of your path. The solution takes 22 moves.

Solution

Want to see the solution to this puzzle?

Let us know what you think of Bogglers: E-mail alternate solutions, comments, and suggestions to bogglers@discover.com.

Got new solutions for the puzzle? Want to see other people's solutions? Talk to the puzzle master in his discussion forum at www.scottkim.com.

Adrian Fisher and Mazeworks have introduced "Celtic Knot Puzzle Playing Cards"; see www.mazemaker.com. The Bath maze appears in Fisher, Adrian, and Howard Loxton. Secrets of the Maze. London: Thames and Hudson, 1997. The quilt maze appears in Abbott, Robert. SuperMazes. Prima, 1997, available at logicmazes.com.