Country Road (puzzle)

Country Road is a logic puzzle by Nikoli.

Rules

The square grid is divided into "rooms" of various shapes; some of these rooms contain a number. The object is to draw a closed loop in the grid, entering and exiting each room once. A room with a number must have that many squares used by the loop (a room without a number may have any number of its cells used). Lastly, orthogonally adjacent unused squares must not be in different rooms.

Strategies

• Rooms with given numbers of cells are often a good starting point, especially if they have as many cells used as cells in that room.

• Rooms that are only adjacent to two other regions must connect to those two other regions. If those two other regions connected, that would form a smaller closed loop than required, so they cannot connect with each other, and so one can mark any common borders of those rooms as "unused".

• Marking in impossible places for loop segments can eventually lead to certain cells being unused, and so orthogonally adjacent cells in other regions being used.

• As with many loop puzzles, a corollary of the Jordan Curve Theorem (i.e. any two closed loops must intersect an even number of times) can help determine whether a loop segment is used or not.

Variants

• In one variant of Country Road, not all rooms must be used. Naturally, all cells next to an unused room are part of the loop.

External links

• Nikoli's Japanese page