Sudoku: love it, hate it

I have a logical cast of mind. I am not boasting that I am good at logic and a whiz at solving logical problems and puzzles, merely stating how my mind works, something I have discovered over the years. Women are often regarded as “intuitive” and non-logical. Without getting in arguments about gender stereotyping, I think these are the two main ways that human minds work to deal with problems and life in general: some people are “intuitive” (i.e. “imaginative” or “creative”) and others are “logical” (i.e. their preferred problem solving strategy is an algorithmic one).

Though I have my occasional imaginative moments, I am a fully paid-up member of the second group. In our family I do the arithmetic, sort out the bills, work out how much money we have left til the end of the month and so on. Set me a problem and I will spend far longer working out a method for solving it than actually solving it. The solution might be obvious, but I still want the security of knowing there’s a method that justifies the obvious solution. On the other hand, give me a simple choice – what do I want for Christmas, where shall we go on holiday, do I want to eat Indian or Chinese tonight – and I go to pieces.

Being a logical type thus has advantages and disadvantages. I often see the solution to a problem when others are still arguing and debating and getting nowhere. If there is a logical answer to a question, I will get there in the end no matter how long it takes because I am dogged in pursuit of solutions. This may well be a characteristic of logical people. On the other hand, people often accuse me of being unsubtle, dogmatic, cold-blooded, etc. because once I have found the solution, being commanded by logic, I am not easily persuaded to abandon it or to modify it.

Another difficulty is that not all problems in life can be solved logically. I am often amazed when Tigger solves in a trice what is for me an intractable problem. In that way, I suppose we make a good pair, each specializing in a particular sort of problem.

It is therefore rather amusing that it was Tigger who introduced me to sudoku. Tigger has one of those jobs where you are frantically busy one moment and twiddling your thumbs the next. So she took up sudoku. I was uninterested at first but gradually got into it. When I go down to meet her from work, I collect two copies of the freebie London Paper, one for each of us. If there’s a copy of the Metro lying around, I pick that up too. When I get to Tigger’s workplace, she hands me a copy of City A.M.

The London Paper contains 3 sudoku puzzles, labelled “Simple”, “Medium” and “Difficult”, respectively. I find the simple one very simple (which doesn’t mean I never mess it up, which is easy to do when you’re over-confident) and the medium is quite easy too. In contrast, I rarely manage the difficult one. I like the City A.M. sudoku. I couldn’t finish these at first but regularly complete them now, although they take me a while. I must have learnt something.

What is the connection between sudoku and my logical mindset? You might think that doing a sudoku puzzle is an exercise in pure logical thinking and therefore ultimately boring. I agree that in the case of the simple ones, this is true. The more difficult ones, however, require a higher order of thinking. The more you do, the more little tricks you learn and that can be fun. The reason why I hate as well as love sudoku becomes apparent in the more difficult ones. In these, logic isn’t sufficient. You have to use a technique called “Ariadne’s thread”. Put simply, this involves trying out numbers in squares and if this doesn’t work, changing them and trying something else.

I give up at this point because to my mind, it’s no longer a logical problem but a game of trial and error. Secondly, because each choice entrains other choices, your trial and error can become very complex. This is an example of a group of problems know to the A.I. community as A* (pronounced “Ay star”). The archetypical problem of this class in the Travelling salesman’s problem.

Imagine a travelling salesman who has to visit a list of towns and return to the starting point. He can visit the towns in any order and he knows the distances between them all. The problem is to work out the shortest route that visits all the towns. It sounds easy, doesn’t it? For two or three towns it is: just try all possible combinations and select the shortest one. But as you add towns, the possible number of routes increases exponentially. With relatively few towns you arrive at so many combination that no human could ever try them all (life is literally too short) and even the fastest computer couldn’t do it, either. In other words, this is an intriguing group of problems for which there is a perfect algorithmic solution, guaranteed to find the answer but the process simply takes too long for anyone ever to do it.

I doubt whether any sudoku puzzle would ever be that complex. No, it’s just that my mind rebels at trial-and-error methods. I like clean, guaranteed algorithmic solutions. That is both my virtue and my vice.


About SilverTiger

I live in Islington with my partner, "Tigger". I blog about our life and our travels, using my own photos for illustration.
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9 Responses to Sudoku: love it, hate it

  1. Baralbion says:

    I, too, tend toward the rational, altough I don’t think I’ve ever had the patience to finish a sudoku puzzle. But it’s not black and white, is it? Most of us are somewhere between the extremes on the rational/intutive spectrum. And it is surely possible that there are some talented individuals who are both very rational and very intuitive. Equally, there must be some who are neither.

    Now, here’s a rational question. How many possible sudoku puzzles are there? It must be a finite number, mustn’t it?

  2. SilverTiger says:

    Yes indeed, we all have rational and intuitive features. We probably couldn’t function normally unless we did. We have all met people who “take everything literally” and they have difficulty making sense of the world, especially human relationships.

    I don’t know how many possible sudoku puzzles there are nor how to work it out. By “puzzles” I take it we mean filled-in grids. That basic number would be multiplied by the number of arrangements of each one according to how many and which numbers are removed when turning the grid into a puzzle.

    In books and articles, the number of sudoku puzzles is usually stated to be “millions” but I have not seen a more exact answer than that.

    It is not a case of simply working out how many arrangements of the numbers 1-9 you could put in all rows or columns. I think that would be easy. For a row it would be n = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 and the final answer would be n raised to the ninth power.

    The problem is that this simple calculation doesn’t work because the position of every digit is constrained by the position of every other digit. It isn’t a free choice for each digit.

  3. SilverTiger says:

    Thanks. I’m glad to see someone has actually solved it. Mind you, it is the sort of problem that would intrigue a mathematician.

  4. Zachariah says:

    Does anyone know where to publish a Sudoku research paper?

  5. Beth says:

    Hi, I googled this page and hope you still keep an eye on things? Firstly, I would like to say that I know exactly what you mean about the DIFFICULT puzzle in the London paper being hard to finish. Simple reason is, its in the top league of ability (thats a nice thought) and secondly it cannot be completed without the further logic applicable to what they call ‘locked candidates’. I have just worked out what on earth all this means and how to ‘get unlocked’. Let me tell you, it is a truly emancipating experience (dinner will finally be cooked, the dog will finally be taken out). You might think about downloading an excellent program like ‘sudoku dragon’ which has a really neat tutorial section. Basically your problem is to work out which squares prove the PERMUTATION RULE. You need to find all your ‘naked singles’ your ‘hidden twins’ and the like. Thank you GOD for Sudoku…..!
    All the best

    • SilverTiger says:

      Thanks for the information, Beth. I had realized that there must be “higher rules” involved in solving these more difficult puzzles. I do sometimes manage to solve the difficult one in the Metro, say about one in 10, which is an improvement on my past performance! But I guess that it is because these are in the lower range of difficulty and can be solved with my usual techniques plus noticing some little feature or other.

      You provide material for further research so who knows: I might yet crack the difficult sudoko after all! 🙂

  6. hodge says:

    you need to use techniques known as X-WING and SWORDFISH to complete the ‘difficult’ grid in londpaper…..

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