No not that. Naked Sudoku is what I call the process of solving a Sudoku puzzle without writing anything in the puzzle area except the final answers. The possibility of using a title to attract extra eyeballs to read this post never entered my thoughts.
Slow beginnings
I learned Sudoku the way many others probably did – you wrote small candidate numbers in each square and then applied logic rules to reduce the candidates to a single one which became the answer. Of course, it doesn’t take long before some of the answers become pretty obvious so this process gets short-cut and more final answers get written in directly. Penciling in candidates starts to happen later and later in the puzzle.
Doing this became a hassle for me as finding the pattern in the candidates requires good penmanship and good eyes. I started to photocopy-enlarge the Sunday paper Sudoku puzzles so that (a) the senior Sudoku-solver in the house could show me how fast she could do it and (b) I would have more space to write in candidates.
That was fine for a while, but I still found that some puzzles ended up with a final phase that I called a “slog”, where many of the cells started with 5 or 6 candidates pencilled in, and reducing them involved slogging through looking for patterns. When I started looking for better ways of solving, I came across two things. One was a plethora of complicated rules for special situations, with names like “X-wing”, which I could never remember, and the other was Snyder notation from Cracking the Cryptic YouTube videos.
Using this notation, the solver only writes candidate numbers in a 9×9 box if there are exactly two places where they can go, so there are a lot less numbers. I thought this was going to solve my issue with untidy little numbers everywhere, but it didn’t. However, it probably did pave the way to finally coming to peace with Sudoku puzzles.
More fun, less slog
I realized that if I wanted to memorize a complicated set of rules I’d rather use my brain power to write a program to solve Sudoku. Then I realized that this had already been done. So if I wanted a mental challenge which was also fun, why not try to solve simpler puzzles, but mentally – i.e. without any pencil marks.
This turned out to have a number of advantages:
- “Seeing” the numbers was a lot easier, as each cell was either a number or empty. In particular, it’s much better for spotting all of the locations for one particular number.
- With nothing written down, it’s necessary to “re-compute” candidates many times, so one gets a lot of mental exercise
- It’s a lot more fun developing a strategy for puzzle-solving than understanding and then memorizing someone else’s process!
I’ve found that I can now hold up to five or six candidate numbers in my head while examining each in turn to see if it is a solution for a particular cell. Typically I’ll determine the missing numbers in a box and see if the other numbers in the row or column eliminate it from contention or determine that it is the only possible solution. I find this easier than looking at a cell and stepping through all nine numbers checking the surrounding box, row and column each time.
I’m also getting better at looking at a nine-number group and quickly determining which numbers are missing, although I find this easier to do in a box, harder in a row and still harder in a column.
I’ve developed a process that I think of as “lowest-hanging fruit” which solves a puzzle in three stages.
Lowest-hanging fruit
The principle is to look for the easiest thing to do next.
Third Box Check
In stage one, or “Third Box Check”, I look at a row or column of three boxes and find places where the same number occurs in two boxes leaving only a single cell in the third box where the number can go.
Intersecting Boxes
In stage two (“Intersecting Boxes”) I cycle through each number (1 to 9) and look for a box that lies on the intersection of a row of boxes, one of which contains the number and a column of boxes, one of which also contains the number. Then I see if enough empty spaces are eliminated in the target box so that only one is left for the number to be written in. Phase two is similar to phase 1 but in two dimensions. Often, the result is not a single cell available, but two of them, and if they are in the same cell row or cell column, then that fact can be used in another intersection or a Third box Check.
Intersecting Boxes also acts as a double check for numbers missed in stage 1, either from not seeing, or because with extra cells filled in, there are more opportunities for Third Box Check solutions to appear. Intersecting Boxes can also be repeated later in the solution if there is an impasse.
What’s missing?
Stage three shifts from “where is the only place I can put an X” to “what is missing in these cells”? This is taking a group of nine cells, seeing what numbers are missing and looking for reasons why a missing particular number either must go or cannot go in a particular cell. I usually scan for the groups with the fewest holes and do these first. This is the thinking part of Sudoku, and my process doesn’t bring any particular insights to this stage, except that the more numbers one can enter before reaching this stage the easier it will be. However two processes will be handy in this stage:
Whenever a solution is written in, I immediately perform a recursive Third Box Check on that number, in both directions (row and column). By recursive, I mean that if a check provides a solution, then do it again from the new solution’s location, and so on. Often this will result in circling the puzzle, filling in four five or six new solutions. If the original solution created two or more numbers, then do the recursive Third Box Check on each of the other numbers as well.
My personal preference is to ignore other opportunities as I go through the process. This drives the senior solver crazy, when I don’t stop to fill in a single empty square in a group. Apart from the fact that I sometimes don’t see these, I find that it’s hard enough to follow through on the Third Box Checks for every solution without taking a sidetrack and then coming back. I also find that I make less mistakes doing a Third box Check than I do determining which number is missing, so the more numbers I fill in correctly, the less white-out I have to use. However, towards the end of a puzzle this is probably a moot point.
Naked Sudoku will not work for every puzzle, and there will be some where there is no alternative than to start pencilling in candidates and slogging through, but it’s possible to solve the majority of puzzles published in a newspaper, and think how smart you will feel when you do it “the hard way”. No need to tell anyone that it might even be easier!
