# SudoCue - HaniDoku Solving Strategies

### Scanning

You start solving a HaniDoku by scanning the grid. Use the information that is given to you by the digits already placed in the grid.

 When you place a digit, all cells that share a line with this cell can no longer contain this digit. This picture shows a 5 in R4C3. There are 20 peer cells that no longer allow digit 5, because they share a line with R4C3. These cells have been marked with a red background color. Please notice that the number of peers is different, depending on the location of the cell. Cells on the edge have 16 peers and the cell in the center has 24 peers. Here is a digit 8 placed near the edge. This placement not only eliminates candidate 8 in all peers, but you can also obtain more information from this placement. Because digit 8 is placed in the red line of size 5, it must contain a range that includes digit 8. There are only 2 possibilities for a line of size 5: 45678 and 56789. The line can no longer contain digits 1, 2 or 3. All candidates for those digits can be eliminated from the red cells. The orange line of size 6 can no longer contain digits 1 or 2. These candidates can also be eliminated. In the green line, digit 8 is present in both ranges. No eliminations in the green cells are possible, other than the candidates for digit 8.

### Naked Singles

In an empty HaniDoku grid, all cells can contain digits 1 through 9. We call these the candidates for each cell. By scanning the grid, several candidates are eliminated, either because a peer already contains the digit, or because a value placed in a peer puts the candidate out of range. When 8 candidates in a cell have been eliminated, the last candidate is a naked single. You can safely place the digit in the cell, because there are no other possibilities left.

To detect naked singles, you may want to use pencilmarks. Write the remaining candidates in the cell with a pencil in small digits. When you play HaniDoku using HaniCue, use the Markup tool to show pencilmarks in the grid. Do not use pencilmarks for easy puzzles. They spoil a lot of the fun, because there is nothing left to search.

### Hidden Singles

When a line has a single candidate left for a mandatory digit, we say that there is a hidden single in that line. Beware of the mandatory digit restriction. Optional digits cannot be hidden singles, because it is also possible for the line not to contain that digit. This is a big difference with regular Sudoku.

A digit is mandatory in a line when all possible digit ranges contain that digit. Our main page contains more background information on mandatory and optional digits.

When you are playing HaniDoku with HaniCue, use the Filter buttons to highlight all remaining candidates for a particular digit. This will help you find lines with a single candidate, but you need to make sure that the digit is indeed mandatory in the line before you decide to place the digit in that cell.

### Naked Subsets

You can use a technique like naked subsets in the same way you would use it in regular sudoku. Read more about naked subsets in the SudoCue Solving Guide.

Because there are no boxes, you cannot use regular sudoku techniques like locked candidates. To compensate this loss, you will discover new solving techniques in HaniDoku.

### Triangulation

 This picture shows how you can use the new Triangulation technique. You see 2 candidates in =8= for a certain digit. This digit must be mandatory in this line, otherwise the technique cannot be used. This is a strong pair. One of these two cells will contain the digit, but we cannot be sure which it will be. However, when we can draw a triangle with 3 equal sides using these 2 cells, the 3rd cell in that triangle cannot contain this digit. It has a red color in this picture. Triangulation can be done on both sides of the line. The red candidate can be eliminated. Remember that the digit must be mandatory in the line containing the strong pair (green cells in the picture). The digit can be mandatory or optional in the other 2 lines that form the triangle.

### Hourglass

 This picture shows how you can use the new Hourglass technique. This time, there are 2 strong pairs in lines =3= and =8=. The cells are confined to /5/ and \5\. Because both of these lines will have this digit in either =3= or =8=, the digit cannot be placed anywhere else on these ascending and descending lines. The candidates that you can eliminate are marked in red. This technique is very similar to X-Wing in regular sudoku. It even looks more like an X-Wing than the original. As with Triangulation, the strong pairs must be be located on lines where the digit is mandatory. Please notice that this technique can also be used with ascending or descending lines containing the strong pairs (the top and bottom of the hourglass).

### Gateways

This technique uses the fact that an optional digit can have a prerequisite digit to form a valid sequence.

(189) (1278) (35) (45) (345) (6)

Examine this list of candidates for a line of size 6. Digit 6 is placed. Digits 345 form a disjoint group which makes them mandatory. Digits 1, 2, 7, 8 and 9 are optional.

The second cell contains the only candidate for digit 2. If we would place digit 1 in that cell, there would not be a candidate 2 left, making it impossible to obey the rule of consecutive digits. Candidate 1 in the second cell can be eliminated.

Because digit 3 is mandatory, digit 9 can be eliminated from this line. To use digit 9, the sequence must be 456789. You can also eliminate digit 9 using the Gateway technique. To be able to place digit 9, you need digits 7 and 8. There are only 2 cells that have candidates for these 2 digits, so digit 9 cannot be a candidate in its gateway cells. This removes candidate 9 from cell 1 and thus from the entire line. Now try to perform a Gateway reduction for digit 8.

Here is a formal definition of the Gateway technique:

When an optional digit D has N prerequisite optional digits, and all candidates for these prerequisite digits are confined to N cells, digit D can be eliminated from these N cells (the gateways).

### HiLoLo - HiHiLo

No, this is not a line from a song, but a technique which is a simple variation on Gateways. This pattern can be found quite often in the endgame, when the middle digits 4, 5 & 6 have been placed throughout the grid.

(4) (5) (6) (37) (27)

Here we have 2 cells with 3 candidates. Digit 3 is a prerequisite for digit 2. When we place digit 7 in the (37) cell, the other cell only has candidate 2 left. This is invalid, because in placing the 7, we eliminated the last candidate for digit 3. This HiLoLo example has one high and two low digits, but this technique can also be applied with two high digits and one low digit. That is the HiHiLo alternative.

Here is a formal definition of this technique:

When an optional digit D1 has a prerequisite digit D2, any candidate can be eliminated that would remove the last candidate for D2 and at the same time expose digit D1 as a naked single.