Hashi

From Puzzlewiki

Hashi, or Hashiwokakero, is an abstract logic puzzle that consists of determining a network of bridges given a grid of circles with numbers in them.

The puzzle consists of circles that contain numbers (from 1 to 8). The solver must connect circles with lines so that:

• There are 0, 1, or 2 bridges connecting circles.
• The circles and bridges form a single network.

Solving Techniques

Solving typically begins by starting with circles that must have at least one bridge in each possible direction. Examples are:

• Corner circles with 3 or 4. A corner circle is any circle where you can only reach another circle in 2 of the 4 possible directions.
• Edge circles with 5 or 6. An edge circle is any circle where you can only reach another circle in 3 of the 4 possible directions.
• Inner circles with 7 or 8. An inner circle is any circle where you can reach another circle in all 4 possible directions.

A special set of circles are the 1-3-2 configuration, as defined by Thomas Snyder. The 3 must be an edge circle (see above). Give this set of circles, there must be a bridge connecting the 3 to the 3rd circle (not the 1 or 2). See the illustration below.

Another special set of circles is a ?-2-2 configuration, where the middle 2 is a corner circle. In this instance, there must be a bridge connecting the ? and middle 2.