The addictiveness of Sudoku puzzles

Why are many people addicted (in a good way) to Sudoku puzzles? There are no clear-cut answers to this, hence we have postulated our own hypothesis. This section is dedicated to our speculation about the reason for the addictiveness of Sudokus.

Let us first look at how gaming apps are designed to be addictive to understand the addictiveness of Sudokus. What we know about gaming apps is that the difficulty level progressively ramps up from easy to frustratingly hard in a short period of time. With little effort and skill, the players are able to score points at the outset. The earlier wins keep the gamers hooked through the more difficult phases. After enjoying success, they are thirsty for more even if the earlier success was due to luck more than talent.

Next, we consider the maze.  When solving a maze, you could trace out a path that brings you close to the exit and still nowhere close to finding a solution. You really have nothing except failed attempts and wrong answers until you have the correct final and full answer. Even worse is that you do not know if you are on the right path until the whole puzzle is solved. That is not the case with Sudokus, where a win (filling a free cell) is a win. You will not need to redo a win just because you cannot solve the entire puzzle. That may be one of the best things about the Sudoku. Your wins are clear and verifiable even if you cannot solve the whole puzzle.

In Sudokus, the level of difficulty can follow this path: a) easy; b) hard and slow; and finally, c) easy and fast. All Sudokus have stage c), and most Sudokus also have stage b). However, this is the key point — not all Sudokus have the first stage, a).    The ones that do have stage a) are especially addictive, because they allow the readers to score some quick and easy wins. The clear and verifiable progress and the presence of stage a) is what makes some Sudokus so addictive.

This brings us to the next and crucial point. In this book, the puzzles have been chosen so you have at least one quick easy win, i.e., each puzzle has stage a). Each puzzle was chosen to satisfy the following condition: the existence of at least one free cell for which the answer can be obtained using an application of cell logic alone. These cells are called addictive cells. You may recall that cell logic requires that there can be only one instance of any number in the row and column and box to which the cell belongs. In the Sudoku on Page 1, the free cells, R9C8 and R9C2 are not addictive, but R1C6 and R3C1 qualify as addictive cells.

We can rank free cells based on how addictive they are.

Addictiveness of Rank 3

A free cell that can be filled because the row or column or box to which it belongs already has 8 numbers is the most addictive. Let us give it a rank of 3. R1C6 on page 1 has rank 3, because the numbers in row 1 already use up 8 numbers, leaving us with only one number, 9, for the cell. So, R1C6=9

Addictiveness of Rank 2

Next, consider a free cell (e.g., R2C4) that can be filled because a combination of [Column and Row] or [Box and Column] or [Box and Row] to which it belongs already contain 8 numbers.  Such a free cell has an addictive rank of 2. For example, R2C4 has the numbers [2,5,6,8,9] in Row 2 and [1,4,7] in Column 4, leaving us with only one number, 3, for the cell. So, R2C4=3.

Addictiveness of Rank 1

Next, we consider a free cell that can be filled because 8 numbers are filled by the combination of [Row and Column and Box] to which it belongs. This free cell (e.g., R7C5) has a rank of 1. The number [3] in Box 8 + numbers [2,4,5,6,8] in Row 7 + numbers [1,7] in Column 5 give us 8 numbers out of 9, leaving us with only one number, 9, for the cell. So, R7C5=9.  

Addictiveness of Rank 0

Finally, we have free cells that have a rank of zero, which means they are not addictive at all. In the above puzzle, R9C8 has a rank of zero.

The puzzles in this book have been chosen so that there is at least one free cell for which the answer can be found using the simplest application of the rules of logic. If you need any help solving the puzzles, two hints per puzzle are provided in the hints. The hints show the most addictive cells in each puzzle. These easy wins will give you confidence as you tackle the other cells