TECHNIQUES FOR SOLVING GOKIGEN PUZZLES

There are rather a large number of strategies which can be used when solving GOKIGEN puzzles. Fortunately, most of them are quite simple to understand. Some might even say that they are obvious.

When specific cells need to be referred to in this discussion, they will be designated as C4-R3 which means the 4th cell in row 3.

For a description of GOKIGEN puzzles, refer to  Building Gokigen Puzzles 

Five Simple Strategies.

   
These strategies are all quite obvious, but are included for the sake of completeness. They are given without explanation or justification. Examples of these strategies will only be found in quite simple puzzles.
  • 1 in a corner. Cell C1-R4.

  • 0 in a corner. Cell C4-R4.

  • 0 on the boundary. Cells C4-R1 and C4-R2.

  • 2 on the boundary. Cells C1-R1 and C2-R1.

  • 4 in puzzle. Cells C2-R2, C3-R2, C2-R3 and C3-R3.


Forced Diagonal Strategy.

   
There are two variants to this strategy.
  • When a circled number is exactly equal to the number of diagonals which are available. See C1-R2 and C1-R3 for an example.

  • When a circled number already has its required number of diagonals, then additional diagonals must be drawn so that they do not converge upon it.

    See C3-R4 for an example.


Avoid Loops Strategy.

   
At this point, there are only two cells remaining to complete the puzzle. In both cases, a loop will be created if the diagonal is inserted in the wrong direction, and this must be avoided. In this example, the loops are of minimal size, but in practical puzzles, the loops may be much larger, and more difficult to identify.

Multiple Ones Strategy.

   
There are three strategies which involve circled ones. They are given without justification. If you take a pencil and paper and doodle for a while, you will easily see that these strategies are logically sound:-
  • When the circled ones occupy opposite corners of a cell, the diagonal must be drawn so that it does not join the two circles. Two examples are shown at C3-R3 and C4-R3.

  • When two circled ones are adjacent to each other either horizontally of vertically, four diagonals may be inserted immediately as shown at C2-R5, C2-R6, C4-R5 and C4-R6.

  • An extension to the previous strategy occurs when the two ones are separated by one or more circled twos. Once again, four diagonals may be inserted immediately as shown at C2-R2, C2-R3, C5-R2 and C5-R3.

Multiple Threes Strategy.

   
There are two strategies which involve circled threes. They are given without justification. If you take a pencil and paper and doodle for a while, you will easily see that these strategies are logically sound:-
  • When two circled threes are adjacent to each other either horizontally of vertically, four diagonals may be inserted immediately as shown at C1-R3, C1-R4, C3-R3 and C3-R4. A second example can be seen at C5-R3, C5-R4, C7-R3 and C7-R4.

  • An extension to the previous strategy occurs when the two threes are separated by one or more circled twos. Once again, four diagonals may be inserted immediately as shown at C1-R1, C1-R2, C4-R1 and C4-R2.