Sample Problems

Easy

Easy

 

Medium

Medium

 

Hard

Hard

 

Extreme

Extreme 1

Extreme 2

 

 

Descriptive Color Scheme

To aid in understanding, the following color scheme is used in the diagrams:

- A group of interest is shown in pale blue
- Cells of interest are shaded pale yellow
- Completed cells are shaded green
- Excluded cells are shaded gray
- Target number cells are shaded blue
- Pairs are shaded rose
- Triples are shaded rose
- Constraints are shaded blue
- Extreme strategy cells are shaded red
- Exclusion cells are shaded pale orange

Note: pairs may also be shaded pale orange or yellow to distinguish from other subsets
 

Sample Problems General Information

The approach taken with the step-by-step solutions is to use strategies that are appropriate to the level of development associated with the difficulty level of the puzzle. For example, a beginner will likely be working on easy puzzles and will only be able to apply the Single Possibility strategy from Chapter 2 and the Row, Column, and Box Check strategies from Chapter 3. So the easy puzzles are solved only using those strategies.

The step-by-step solution boards are presented in the actual sequence I used to solve the puzzles. I can only describe one path to the solution, and it is not necessarily the fastest or most efficient path. I sometimes jump between strategies when solving these puzzles. While I advocate a systematic approach, I also advocate solving cells as soon as a solution becomes apparent since solving cells often helps solve other cells. If you try to solve the puzzle yourself and follow a different path, your solution will be equally valid as long as your logical process is correct.

The approach I advocate involves selecting a group and working to find the solution to cells within the group or working to find the location of a target number in the group. The group selected for analysis is highlighted. An exception is the Box Exclusion strategy where highlighting the box is not practical since gray shading is used to indicate cells that cannot contain the target number in the box. The shading starts from the target number being used, which is shaded in blue, and extends to the box being checked.

For row, column, and box check strategies, filled cells that are helpful in reducing possibilities are highlighted in yellow.

When a solution is found, the cell is shaded green and the solution number is placed into the cell.

Once a strategy has been applied to solve a cell, other cells may become immediately solvable using the single possibility strategy and taking advantage of available clues. Solutions that follow from the clues are shaded green but the cell solutions are not filled in. This is done to allow you to better understand how the clues are used to find these additional solutions.

In the sidebar I describe the primary strategy used for each diagram and may include hints regarding the position. On diagrams where multiple solutions can be found, cell solutions are listed in the order that they occur. The next diagram will contain all the solutions from the previous diagram. I recommend that you work through these solutions yourself to see how the clues get used to find solutions.

Other cells of interest are shaded in different colors to indicate cells that formed a pattern such a naked pairs, triples, quads, or constraints or cells where the clues were updated.

Extreme Puzzles

Extreme puzzles are solved using the same approach as medium and hard puzzles, with the Box Exclusion and Row, Column, and Box Check strategies the most useful to get started. With extreme puzzles you will more rapidly reach a point where you need the Pairs, Triples and Quads strategies from Chapter 4. The constraint strategies in Chapter 5 can be very useful as an extra tool to help find solutions. The more advanced techniques presented in Chapters 6 through 11 are only required on a few occasions for the most difficult puzzles after all other strategic options have been tried.

Four extreme puzzle solutions are provided. I’ve included more extreme puzzle solutions than any other level since they are more interesting and varied, and of course more difficult with fewer branches that lead to the solution.

The extreme solutions make very little use of the advanced patterns from Chapters 6 through 11 because they patterns are not usually required by the puzzles published in newspapers and magazines.