We tend to use analogies when we are discussing certain topics, introducing new concepts, or simply presenting an abstract idea. Analogies are intended to serve as a model that people understand, can relate to or identify with, and, more importantly, remember. Our challenge is to identify a simple model that can be used to teach people to identify and solve problems – a core competency requirement for lean.

We have learned that teaching people to see problems is just as important as teaching them to solve problems. Our education system taught us how to use the scientific method to solve problems that were already conveniently packaged in the form of a question or modeled in a case study. Using case studies for teaching is typically more effective than traditional “information only” or “just the facts” methods. (The government of Ontario is presently considering a complete overhaul of the education system using case studies as a core instruction method.)

The effectiveness of any training people receive is compromised by time – the retention span. Our school systems are challenged by this at the start of every school year. Teachers must re-engage students with materials covered in the last semester or topics covered prior to the break. In business we may be too eager to provide training at a time when current business activities are not aligned for the new skills to be practiced or exercised. A commitment to training also requires a commitment to develop and routinely exercise these skills to stay sharp.

One of the fundamental rules of engagement for lean is to eliminate waste, where value added activities are optimized and non-value added activities are reduced or eliminated. Although it may appear that we have identified the problem to be solved, in reality we have only framed the objective to be achieved. We understand that the real solution to achieving this objective is by solving many other smaller problems.

**The Sudoku Analogy – A Model for Finding and Solving Problems**

A favourite past time is solving Sudoku puzzles, the seemingly simple 9 x 9 matrix of numbers just waiting for someone to enter the solution. The reasons for selecting and recommending Sudoku as an introductory model for training are as follows:

**Familiarity:**Sudoku puzzles are published in all daily newspapers and numerous magazines and they have become as popular as cross-word puzzles. Most people have either attempted to solve a puzzle or know someone who has.**Rules of Engagement:**the rules of the game are simple. Each standard Sudoku puzzle has 9 rows and 9 columns that form a grid of 81 squares. This grid is further divided into nine 3 x 3 sub-sections. The challenge is to enter the digits 1 through 9 into the blank spaces on the grid. Every row, column, and 3 x 3 sub-section of the grid must contain one and only one of each digit. We refer to these as “rules of engagement” as opposed to “framing the problem”.**Degrees of Difficulty:**Sudoku puzzles are typically published in sets of 3 puzzles each having varying degrees or levels of difficulty. Each level typically requires more time to complete and requires the player to use more complex reasoning or logic skills. The claim is that all puzzles can be solved.**Incremental or Progressive Solutions:**Sudoku solutions are achieved incrementally by solving instances of smaller problems. In other words, the solution builds as correctly deduced numbers are added to the grid. New “problems” are discovered as part of the search for the final solution.**Variety:**every Sudoku game is different. While some of the search and solve techniques may be similar, the problems and challenges presented by each game are uniquely different. Although the rules of engagement are constant, the player must search for and find the first problem to be solved.**Single Solution:**a multiple number of solutions may appear to satisfy the rules of the game, however, only one solution exists. Learning to solve Sudoku puzzles may be a challenge for some players, however, even seasoned Sudoku players can be stumped by some of the more advanced level puzzles. To this end, they are ever and always challenging.**Skill Level:**Sudoku puzzles do not require any math skills. Numbers are naturally easier to remember and universal. Letters are language dependent and the game would lose international appeal.**Logical:**deductive reasoning is used to determine potential solutions for each empty square in the grid. As the game is played, a player may identify a number of potential solutions for a single square. These final solution will eventually be resolved as the game is played.

**In practice**

We recommend introducing the team to Sudoku using an example to demonstrate how the game is played. It is best to discuss some of the strategies that can be used to find solutions that eventually lead to solving the complete puzzle. The Sudoku model will allow you to demonstrate the following ten objectives:

**Look for Options:**The solution for the problem to be solved may consist many other smaller problems of varying degrees of difficulty.**Break down the problem:**There may be more than one problem that needs to be solved. Every Sudoku puzzle represents many different problem instances that need to be resolved before arriving at the final solution. Each incremental solution to a problem instance is used to discover new problems to solve that also become part of the overall solution. This may also be termed as progressive problem solving.**Multiple solutions – One Ideal:**There may be times where more than one solution seems possible. Continue to solve other problems on the grid that will eventually reveal the ideal single solution.**Prioritizing:**more than one problem instance may be solvable at the same time, however, you can only focus on one at a time.**Focus:**Problem solving involves varying states of focus:- Divergence: Expand the focus and perform a top-level search for a problem from the many to be solved
- Convergence: Narrow the focus on the specific problem instance and determine the specific solution.

**Test and Validate:**Every problem instance that is solved is immediately verified or validated against the other squares on the grid. In other words the solution must comply with the rules of engagement.**Incubation:**some puzzles can be quite difficult to solve. Sometimes you need to take a break and return later with a fresh eyes approach.**Action:**There is no defined or “correct” starting point. The first problem instance to be resolved will be as unique as the number of players participating. No matter where you start, the finished solution will be exactly the same.**Tangents:**when entering a solution into a square, you may notice other potential problems or solutions that suddenly seemed to appear. It is very easy to digress from the original problem / solution. This is also true in the real world where “side projects” somehow appear to be the main focus.**Method:**There is no pre-defined method or approach to determine what problem to solve first. The only guiding principles for discovering the problem instance to be solved are the rules of engagement.

Lean companies train their teams to see problems and break them down into smaller problems with solvable steps. Sudoku demonstrates the process of incremental or progressive problem solving. Even with this technique it is possible to enjoy major break through events. There are times when even seasoned Sudoku players will recognize the “break through point” when solving a puzzle.

Solve time is another element of the Sudoku puzzle that may be used to add another level of complexity to the problem solving process. Our objective was not to create a competitive environment or to single out any individual skill levels whether good or bad. Lean is a TEAM sport.

**In Summary:**

Sudoku solvers are able to hone their skills every day. Perhaps Sudoku Masters even exist. Imagine someone coming to work with the same simple focus to eliminate waste every day. Although there is no preset solution, we are able to identify and consider any number of potential problems and solve them as quickly as we can. The smaller problems solved are a critical part of the overall solution to achieve the goal.

Most professional athletes and musicians understand that skills are developed through consistent practice and exercise. Repetition develops technique and speed. Imagine a culture where discovering new opportunities or problems and implementing solutions is just a normal part of the average working day. This is one of the defining traits that characterize high velocity companies around the world.

Truly agile companies are experts at seeing and solving problems quickly. They discover new opportunities in every day events that in turn become opportunities to exercise their problem seeing and solving skills. Crisis situations are circumvented early and disruptions are managed with relative ease – all in a days work.

The next time you see a Sudoku puzzle you may:

- be inclined to pick up a pencil and play or
- be reminded of the time you were inspired by the game to solve problems and reach new goals or
- simply reflect on this post and ponder your next break through.

Until Next Time – STAY Lean!