Contents of Key to solution for Slither Link

Key to solution for Slither Link

General rules

Rule of diagonal "32..23"

A combination of previous rules makes new sophisticated rule.

This example shows a case when 2s are put in between two 3s in diagonal line.
Any number of 2s can be put between 3s. There are two 2s in this example.

Let's start by assuming a corner of above 3 has two lines in L-shape as in this figure.
By the "rule of diagonal 2s," this pattern will be copied to below "2s," and the L-shape corner of "2" touches a vertex of below "3".

Since the L-shape line is touching a vertex of 3, you cannot draw lines on two edges of "3" linked to that vertex. This situation conflicts with the rule of this puzzle. Therefore, you cannot have L-shape line on that corner. Only one edge can have a line here.

And the L-shape lines will be drawn at the top left corner of above "3", and the line will be extended to the bottom right vertex toward next "2".

Now, by the "rule of diagonal 2s," a line comes to 3 from star marked vertex. So the two edges on the other side can have lines.

When there is a pattern of 2 and 3 placed as "32..23" diagonally, 3s at both ends of this pattern will have L-shape lines on their outside edges.

Note that the pattern of "diagonal 3 and 3" is a special pattern of this case.

Rule of diagonal "32..23"

Contents of Key to solution for Slither Link