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Diagonal 2's: Diagonal 2's commonly play a special role in Slitherlink puzzles

Diagonal 2's have the ability to transfer effects from one side of the diagonal to the other. Consider the scenario in D3-1, for example. The markings placed around the two 3's in the end result are the same markings that were placed around the 3's in D3.

To test whether a certain scenario does indeed contain diagonal 2's and can thus be simplified to look for clues, we can follow this procedure:

Prodedure 1st Example 2nd Example
1. Look for a set of diagonal 2's.
In the first example, the 2's form a positive slope.
In the second example, the 2's form a negative slope. 		example 1 step 1 example 2 step 1
2.  Draw lines perpendicular to the diagonal that go through the two outside corner points of the diagonal. example 1 step 2 example 2 step 2
3.  Ignore all numbers, marks, and dots in-between the two lines or crossed out by the two lines; then, merge the two remaining triangles. example 1 step 3 example 2 step 3
4.  Since diagonal 2's have the "tranferring" property, we know where marks can be made. example 1 step 4 example 2 step 4
5.  Finally, we can go back and mark the squares in their original positions. example 1 step 5 example 2 step 5

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