Solving Sudoku – Two Group Intersection

Let’s continue with a study of the advanced Sudoku solving techniques. In my previous post, I looked at partitioning the cells of a single group. In this epistle, I look at what you can do with two intersecting groups. In this case, it’s a 3×3 square intersecting with either a row or a column. (If you consider the intersection of a row and a column, you can apply one of the basic techniques.)

Consider the groups marked in green in the following:

We have two groups: a row and a 3×3 square. Look at the three cells that belong to both groups, and consider the value 4. Within the row, the value 4 exists only in the intersecting cells. Within the 3×3 square, the value 4 must exist in one of those two cells that also belong to the row. Therefore, the value 4 can be eliminated from the other cells of the square.

With the techniques described up until now, you have the means at your disposal to solve the vast majority of puzzles. But there are still a few tricks left, which will have to wait until later postings. Next up, we look at the corners of a rectangle.

Hans

Solving Sudoku – Single-Group Partitioning

Okay, so you’ve mastered the basic techniques to solve Sudoku puzzles, and you’re still stuck on a puzzle. At this point, you’ll need to make notes, writing in small print the possible values at the top of each cell. There are a number of “advanced” techniques that can help you progress. At no time should you have to guess at a possibility. All puzzles should be solvable using analytical methods. However, note that most of the advanced techniques only help you to eliminate possibilities. You’ll still need to basic techniques to finish the puzzle. But eliminating possibilities should provide more opportunities to apply the basic techniques.

The technique I describe here involves looking at the cells of one group. Consider the following group with possibilities listed:

Before continuing, have a look to see if you can spot any possibilities can be eliminated.

Note that the values 1 and 2 exist in only two cells in that row, and not in any other cells. Since those two values can only be in those two cells, all other possibilities can be eliminated:

At this point, with those values eliminated, you may find opportunities for applying the basic techniques, allowing you to move forward.

One more note on this particular example: The full 3×3 square at the left is not shown. However, now that we know that two cells of the square only contain the values 1 and 2, we can now eliminate those values from the rest of the cells of that square.

Note that the technique can also be applied with three values. Look for a set of three values that exist in only three cells. All other values in those three cells can be ruled out. Likewise for four or more cells.

In the next installment, I look at an advanced technique involving two intersecting groups.

Hans

Solving Sudoku – The Basic Methods

Do you want to learn how to solve Sudoku puzzles but don’t know where to start? Read on! In this missive, I discuss the basic solving technique.

To start, consider the following puzzle:

Look at the cell marked in blue. An experienced player should be able to look at the puzzle and immediately know what the solution is for that cell. Scan the puzzle above that cell and also to the left. Consider that the value 1 cannot occur in any of the empty cells marked in green. We see that the blue cell is the only cell in the lower-left 3×3 group where the value 1 is possible.

(The keen observer will see another opportunity elsewhere in the puzzle where a 1 must be the solution for a cell.)

While solving a puzzle, as you’re entering values or eliminating possibilities, constantly look for these opportunities since these are the easiest to find.

Okay, so you applied this technique as much as you can and you’re stuck. What next? Consider the following diagram of the above puzzle but with a few values filled in:

Although we can still apply the first technique, let’s see if we can apply the second basic technique. Consider the cell marked in blue. That cell belongs to three groups: a column, a row, and a 3×3 square. Note that the value of the blue cell cannot be the same as any other value in those three groups. So, for that cell, list out its possible values. We see that eight possible values can be eliminated, leaving only one possible value for the cell: 1.

To find opportunities to apply this technique, look for groups with lots of values already filled in.

I’ll leave the rest of the puzzle to you. Click here to print out a clean copy of this puzzle. It’s the first puzzle in that document.

Using these two techniques, you can solve most puzzles published in newspapers and magazines. To practice, try out the Beginner Puzzles. In my opinion, the best way to solve Sudoku puzzles is by pen and paper, relaxing in an easy chair.

When starting out, it may be useful to write in the possible values in small print at the top of a cell, crossing them out as you progress through the puzzle. But with experience, you should be able to apply both of these techniques without making any notes.

In later columns, I’ll cover the more advanced solving techniques. Next up, single-group partitioning.

Hans

Three Disruptive Technologies

This is the column I wrote intended for the May 2017 edition of our church newsletter. Given recent events, that issue will be my last. With that in mind, I decided not to include this column. Instead, I offer it up here, on my own personal blog:

For almost two years, I’ve had the privilege of acting as editor for KUFLinks. In that role, I’ve taken the liberty of writing a monthly column under the banner “Communications”, most of which have been on one particular topic, technological change. In this missive, I look at three pivotal changes, that have been quite disruptive on society.

First, when editing KUFLinks, I use a piece of software called “LibreOffice Writer”, which is well-suited to desktop publishing. This program is a member of a large class of software known as “free software”. Although much of this software is available at no cost, the word “free” primarily refers to freedom. That is, you have the freedom, granted by the software license, to do what you want with it. Either without restriction, or with one specific limitation that in practice doesn’t affect the users of the software. (There is fierce debate between these two camps, but the details are not relevant to this discussion.)

Most of you aren’t aware of this, but free software underlays much of what we do today. The most popular web browsers, Chrome and Firefox, are based on free software. Most of the software running the internet is too, from the operating systems, to the web servers, databases, and content management systems. If you use a smart phone or tablet, you’re using products based on free software. Even the WordPress software running the KUF web site is free software.

Second, let’s go back a few centuries to the invention of the printing press in Europe. This of course led to immense change in European society. Of interest to Unitarians is the story of one man, Michael Servetus, who used the printing press to publicize his views. In doing so, he got a lot of people mad at him, especially the Catholic church. Servetus expected a safe haven from the Calvinists in Geneva, but unfortunately, they too were not happy with him. Later, Servetus came to be considered the first Unitarian.

Third, we come back to the present. Many of us still remember a time without the internet. Looking back, it now seems strange that we had to look up information in books, often having to wait until the chance to visit the local library or book store. In many cases, we had to travel some distance to find the right repository of information. When doing research, patience was definitely a virtue.

But of course today, everything is on-line, often just a simple search away from the convenience of our home, either on a desktop computer, or on a mobile device. And if we want to connect with other people with the same interests or values, that too is a simple matter of pressing few buttons.

I can say a whole lot more on each of these three disruptive technologies, but I’ll leave it at this. For now.

Cheers! Hans

Tangled Webs in Nijkerk

Looking back at my posts in this blog, I haven’t done one of these drop charts in almost two years. First, it takes a bit of work to create one of these charts. But also, I haven’t found much in the way of tangled inter-relationships in my research. About a year ago, I signed up with Ancestry and spent some time on the German side of my family. However, the records for Mecklenburg-Schwerin on Ancestry only go back as far as 1876, and so I soon exhausted their resources. Later, I spent a few months researching distant cousins in the Achterhoek region of Gelderland, but without finding very many tangles.

But once done there, I turned my sights back to Nijkerk, where many of my ancestors lived. My great grandfather Gerrit Moll (1849-1929) was the first Moll born in Nijkerk, but his wife Geertje Beukers and most of her ancestors lived in the town for generations.

This chart explores the inter-relationships between my ancestors and a couple of other families, in particular, the van den Pol family and the van Dronkelaar family. In this chart, ancestors are marked in red. Blue indicates other blood relatives. (It may help to open the image in a new tab or window.)

Let’s start at the left side of the chart. We see my second cousins three times removed Wouter van Werkhoven (1823-1891) and Rengertje van den Pol (1840-1918) married respectively to Evertje van Dronkelaar (1838-1912) and Wolbertus van Dronkelaar (1845-1922). Wouter and Rengertje were first cousins, and so were Evertje and Wolbertus.

The rest of the chart is more complicated. There are five cases of a distant cousin married to a member of the van den Pol family, all descendants of Jacob van den Pol (1770-1860) and Aaltje Koppen (1781-1865):

  1. Gerrit van den Pol (1807-1877) and my first cousin four times removed Aaltje van Werkhoven (1804-1853), married 1939.
  2. Gijsbert van den Pol (1824-1893) and my second cousin three times removed Aaltje van Woudenberg (1821-1897), married 1848.
  3. My second great granduncle Lubbert Beukers (1822-1896) and Hendrina van den Pol (1824-1877), married 1850.
  4. My third cousin twice removed Evert van den Pol (1851-1938) and my great grandaunt Antje Beukers (1853-1934), married 1883.
  5. Jacob van den Pol (1826-1913) and my second cousin three times removed Geurtje van Woudenberg (1823-1885), married 1848,

It is interesting that, although there are many tangled inter-relationships in this chart, there is only one case of cosanguineous marriage, between second cousins once removed Evert van den Pol and Antje Beukers. Their common ancestors are Evert Teunissen and Aaltje Aalts, at the top of this chart.

I’m not done with this area of research, and so there may be more interesting tangles to discover.

Cheers! Hans

A Personal Theology – Heresy and Universal Truth

The following is a short talk I gave at the Kingston Unitarian Fellowship (KUF) back in 2012. Note that although this reflects my opinions at the time, given the changes in Unitarianism during the past five years, I’m not sure if this would be appropriate today at KUF:

I really appreciate the opportunity to give my own personal testimony on the Sunday when the theme is “Freethinkers and Heretics”, because I do consider myself as a freethinker or heretic. Probably many of us here do. When I was young, my mother brought me and my sister to church on Sunday. At first, to the United Church in Collins Bay. Later, to the Christian Reformed Church just a few blocks north of here, presumably because the United Church was not sufficiently orthodox. At that time, I thought I should be a Christian. My first act of heresy, then, was abandoning the faith of my ancestors.

When I first started thinking independently about theology, I thought about the concept of “universal truth”. That is, is there a religion that would apply everywhere in the universe and at every point in time. I quickly came to the conclusion that no Earthly religion could possibly make such a claim. Later, in university, I took a course in world religions. And although Buddhism and Taoism appealed to me in theory, in practice they too seemed to miss the mark.”Freethought”, according to the Wikipedia, is the philosophy that opinions should be formed on the basis of logic, reason, and empiricism, and not authority, tradition, or other dogmas. By that definition, I suppose I am a “Freethinker”. But I’m not really comfortable with the term, probably for the same reasons I’m not comfortable with the term “atheist”. Consider the question of “God”: Science doesn’t really tell us that God doesn’t exist.

Following the scientific method, the most we can say is that God is untestable. And if untestable, there’s always the possibility that there is such a thing. That is, to me, saying that there’s no God seems just as dogmatic as saying there is. Which is perhaps a heresy to most freethinkers.But to be clear, although I can acknowledge the possibility that there may be a God, since it is untestable, I find little use in the concept. Even those who do fervently believe in a God can have vastly different opinions about the deity. And so, at a practical level, I believe we must live our lives assuming there’s no such thing, and use our intellect and compassion to guide us. I like the quote attributed to the Italian heretic Galileo: “I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use.

The way I see it, science is the best tool we have to understand the universe around us. But scientists themselves are the first to admit that science has definite limits. (Or they should be.) While science can model how something happens, it can’t explain why. For example, why do some things seem to happen just when we need them to happen? Often, I want to know if there’s some specific reason for my existence. And, I think many of us have some vague sense of something just beyond our five senses. I know there are no definitive answers to these questions. But that doesn’t stop me from pondering them and considering the possibilities.

I first learned about Unitarianism in the early 1980’s from an article in the Toronto Star, and later, I started attending Sunday service at the First Unitarian Congregation, when Chris Raible was its minister. After a few years, I moved further away and stopped attending. So for a while, I considered myself a “lapsed Unitarian.” When we moved to Kingston in 2010, Sylvana suggested that we check out KUF, and I readily agreed. And soon thereafter, we signed the membership book. We came for several reasons: First, we wanted our daughter to benefit from the religious exploration program. Second, as newcomers to the city, we wanted to meet new people. Third, I liked the idea of a weekly spiritual retreat.

But finally, I come here to be challenged. To me, the most important avenue to personal growth is to stretch the limits of your comfort zone. I don’t just want an environment where people are unconditionally accepting of my beliefs and values. Although we should be respectful of each others’ beliefs, I believe that you honor my beliefs best by understanding them and expressing your thoughtful disagreement with them if necessary.

Lately, I’ve been participating in a number of UU discussion groups on Facebook. On-line, I see a lot of diversity among UU’s. So much so that, when I offer my point of view, I sometimes feel like a heretic. But the way I see it, the diversity is a real strength of Unitarianism. Many of us approach the great questions of “Life, Universe, and Everything” through spirituality. It seems that fewer of us deal with these questions analytically. Can we use analytical tools in matters of faith? I believe we can. For example, I think the validity and usefulness of the “Golden Rule” can easily be demonstrated empirically. And it’s the one principle that practically everyone can agree on regardless of faith, or heresy. And so, the way I see it, the “Golden Rule” is probably the closest we can get to the concept of “universal truth”.

Cheers! Hans

Customer Service and Dieting

For health reasons, Sylvana and I knew we needed to lose weight. And so back in September, we both joined Weight Watchers. Based on our previous experience, we knew this was the best way to meet our goals, and so far, it has been successful. We both still have a ways to go, but Weight Watchers gave us the tools to make it work. And hopefully stick this time.

So a couple of weeks ago, Sylvana went on-line to renew our memberships, but she noticed that WW already automatically renewed us both at the 1-month price. This isn’t what we wanted. We wanted to renew at the 3-month price, which is more economical. Sylvana went to the chat line on WW’s web site. The customer service rep was friendly, and connected her with someone in the billing department, Abdul. Abdul, however, didn’t respond. In spite of several prompts over 20 minutes, there was nothing from Abdul. Sylvana closed the connection, and tried again. Again, she was connected to Abdul. But this time, he closed the connection immediately.

Needless to say, Sylvana was furious. This is an absolutely unacceptable level of customer service. We discussed the issue, and decided it was time to terminate our membership. We decided to stay with the program until the middle of March, but not to go beyond that.

However, the lousy customer service is not the main theme of this blog posting, nor is it the main reason we’re quitting Weight Watchers. WW has changed. The biggest change is a new points program, called “SmartPoints”, replacing their PointsPlus plan.

(As an aside, years ago computer programmers used to have a saying: Whenever Microsoft uses the word “Smart”, be on the lookout for something dumb.)

Some time ago, they had a simple points regime, based on calories, grams of fat, and grams of fiber. The formula was easy to remember, and you could easily figure out the points just by looking at a nutrition label. But almost 20 years ago now, they introduced the PointsPlus program. Instead of counting calories, the formula now counted grams of carbohydrates and grams of protein, giving more points to carbs and fewer for protein. You pretty much needed the WW calculator to properly compute points, or you had to look up the points in their books.

Late last year, they introduced the SmartPoints system. When we joined WW, we knew (or at least should have known) that something new was coming since the books and points calculator for the old plan were available at discounted prices. In the new program, you punch in calories, grams of saturated fat, sugars, and protein into the calculator.

Of course, they claim that the new program is much better, claiming faster weight loss than ever before. However, we have issues with the new program. In the past, they encouraged a slow and steady approach to weight loss since there can be health issues associated with rapid weight loss. And they always advertised their programs as allowing you to eat anything you want. But under the new program, foods with lots of carbs come out with a lot more points. So many more points that many of your favorite foods are now effectively out of bounds. Looking at how heavily carbs are discouraged, I wonder what’s the difference between the SmartPoints program and the Atkin’s Diet?

Sure, limiting carbs is a good idea. But there always has to be balance in any diet. And while it’s a good idea to favor protein over carbs, in our opinion, it’s not reasonable to penalize carbs so much. By denying your favorite foods, you run more of a risk of falling off the wagon, with all the associated repercussions, including the possibility of binge eating.

That said, we will continue with our dieting. This is still too important for us not to continue. We just won’t do it anymore as Weight Watchers members. And we’ll continue following the PointsPlus system.

And just to be clear, we don’t want to discourage anyone from trying the Weight Watchers program. The new plan may well work for some people, just as the old program works well for others. Weight loss isn’t always easy, and you may have to make some effort to find a strategy that works for you.

Cheers! Hans

My Next Musical Instrument?

A couple of years ago, someone asked me what was the difference between the baritone ukulele and the tenor guitar. I couldn’t answer the question since I never heard of a tenor guitar before. Later, I did a bit of research and discovered the answer.

The tenor guitar is a slightly smaller guitar with the neck of a tenor banjo, originally made so tenor banjo players could easily play guitar instead. Like the tenor banjo, standard tuning of the tenor guitar is in fifths, CGDA. However, other tunings, such as DBGE, are also very common. Compared to a baritone uke, the tenor banjo is a bit bigger but with a narrower neck.

Like many other ukulele players, I have a modest collection of instruments. I’ve never really been a fan of the baritone, and so I’ve never been tempted to add a baritone to my collection. But I rather like the tenor guitar. Sometimes, you can find a tenor guitar made by Kala at the local music store, and I must say, it sounds rather nice. It combines the sound you’d expect from a guitar with the ease of playing of a ukulele. I really can’t justify buying a new instrument right now, but I find this instrument very tempting.

So why choose a four-stringed guitar instead of a conventional six-stringed instrument? Think of those two bass strings on a normal guitar, tuned to E and A. For many chords, these strings aren’t used at all. When strumming, many chords require that you don’t touch those strings at all, and yet, they will still vibrate and contribute to the sound. This is fine for some keys, but for others, you really need a capo to avoid dissonant notes from those two strings.

Like a ukulele, the only notes you get out of a tenor guitar are from the vibrations of the four strings. That is, you get a more pure sounding chord. Many guitar players who use just a strumming style of play would get along quite nicely with this four-stringed guitar.

Don’t get me wrong, I love guitar music. The guitar is a very flexible instrument, and can produce wonderful music from a skilled player. It’s no wonder that it’s such a popular instrument. However, many who try it get discouraged and give it up, never bothering to try playing music again. Like ukulele, the tenor guitar should be given more of a chance.

Cheers! Hans

Adventures in Banjo

Is the ukulele a gateway instrument? I suppose many kids who learn ukulele in school move on to guitar, and that’s great. An instrument as easy to learn as ukulele can easily give kids an appreciation for music that can last a lifetime.

As James Hill once said, for middle-aged folk like me, ukulele can be a second chance at music. I started playing uke about seven years ago, and I’ve loved making music ever since. I know I’ll never be good enough to play professionally, but that really doesn’t matter. Ukulele has also been a gateway instrument for me. Ever since I was young, I secretly wanted a banjo. A couple of years ago, I satisfied my long-held desire, and added a banjo ukulele to my modest collection of instruments. As fun as ukulele is already, the banjo uke is even more fun. More recently, I added another banjo to my collection, a tenor banjo.

When most people think of banjo, they think of the five-string banjo, a staple of bluegrass music. While I love bluegrass music, I didn’t want to limit myself to that genre. To me, the four-string tenor banjo offers more flexibility when playing, allowing both strummed and picked styles of playing.

However, the tenor is not as common as the bluegrass banjo. You just don’t find many to choose from in the local music stores, if you can find any at all. I found an inexpensive Trinity River tenor in a local pawn shop, but one poster in an on-line banjo forum recommended against it. But a couple of months ago, while visiting Renaissance Music, I found two tenors, one a used Gold Tone tenor, which I ended up buying.

Note that there are multiple ways to tune a tenor banjo. (Heck, there are lots of ways to tune the bluegrass banjo too.) The standard way is CGDA. But other common tunings include mandolin tuning (GDAE) and “Chicago” tuning (DGBE). The latter is also how you tune a baritone ukulele. When I tried out that Gold Tone tenor in the store, I had a hard time getting what I thought was the A string into tune. When that string snapped at home and I got a new set of strings, I realized that the instrument was tuned to DGBE, not CGDA.

I noticed that CGDA tuning is similar to standard ukulele tuning, GCEA. When I installed the new strings, I reversed the C and G strings, and tuned the D up a whole note. This allowed me to play the tenor using ukulele fingering, while keeping the same range of notes as a standard tenor banjo. But that tuning sounded odd. The difference between the second and third strings was just too great. So I then took the original B string, and replaced the third string, tuning the new string to C. And so I ended up with a banjo tuned exactly like my low-G tenor ukulele. In the future, I may experiment with re-entrant high-G uke tuning on this tenor.

I still have a lot of practicing to do before I play my new toy in public. The frets are further apart and the strings closer together, making left-hand fingering a bit trickier. Like the banjo ukulele, any time you touch the instrument, it makes noise, which has to be controlled. But also like my banjo uke, my new tenor has a resonator that can be removed, which can make the instrument a tad quieter, useful when practicing at home.

Most every month, you can find me performing with my banjo uke at the Kingston Sing-along Society sessions, normally scheduled for the first Friday of the month, at the Kingston Unitarian Fellowship. At some point, after more practicing, I’ll bring my new tenor.

Cheers! Hans

Genealogy – Then and Now

I started doing genealogy back in the early 1990’s. In the early years of my research, I discovered a fair bit of information about my ancestors. But after a few years, other interests grabbed my attention, and I put my genealogy research on hold. Two years ago, twenty years after beginning, I resumed my research. In this tome, I’d like to take a look back and compare how I did genealogy back then with how I do it today.

Back then, I used a DOS based program called GIM. Most programs at the time supported the GEDCOM 3 standard. Today, I use a program called Gramps, which implements fully the GEDCOM 5 standard, still under development in the early 1990’s. As far as I’m concerned, the most important improvement of GEDCOM 5 is robust support for sources and citations. Back then, if you recorded source information at all, it was done using notes. Today, you have no excuse for not including citations in your database.

These days, I don’t add any fact to my database unless I can cite the source. When I restarted my research, one of the first things I did was go through my data, adding sources and citations to every fact. I also cross-referenced my hand-written notes by adding the citation id to every event in my notes. Using a filter in Gramps, I was able to locate every event without a citation. I had to be brutal, but some facts had to be deleted since I had no idea where they came from.

Back then, the general public just started getting access to the internet. This was a great boon to genealogists since it allowed us to better share data. But we still needed to visit the local LDS Family History Center to view microfilmed records, and record the data in hand-written notebooks.

Twenty years later, the technology continues to improve. There are a couple of incredible on-line resources that I take advantage of on a daily basis. The first is FamilySearch.org, which hosts jpeg images of almost all of the LDS’s collection of civil and church records from the Netherlands. Since half of my ancestors were born in the Netherlands, I fully take advantage of this incredible collection. Whenever I find a record of interest, while working at my desk at home, I download the image, crop and scale the image, and then include the image in my database as part of the citation. You can’t support your facts any better than that.

Another incredible resource is WieWasWie.nl, an index site for the Dutch civil registration. There are a few holes in their coverage, such as Gelderland births, but otherwise, it’s the first place I visit when searching for people. As far as I’m concerned, if for whatever reason I can’t find a scanned image of a record, cutting and pasting WieWasWie data into a citation is an acceptable alternative.

For the German side of my research, the on-line resources are still lacking. FamilySearch.org has the images for the 1867 and 1900 censuses of Mecklenburg-Schwerin, which helped me connect with my Ludwigs ancestors. However, to view the Mecklenburg-Schwerin church books, I still need to visit the local LDS Family History Center. It’s a 20 minute drive, and is never very busy. But since the Dutch on-line resources are so much better, I haven’t done nearly as much research on my German ancestors.

There is hope, however. There is an effort underway to digitize the German church books and put them on-line. Hopefully, the site will be as easy to use as FamilySearch.org. And more importantly, I hope that the quality of the scans will be as good. Once the Mecklenburg-Schwerin church books are on-line, I expect to spend a lot of time downloading those records. (Of course, the LDS are working hard digitizing all of their microfilms, but who knows when they’ll get to the books I need.)

Finally, here’s a summary of what’s in my Gramps database as of this morning:

  • Number of individuals: 8196
  • Number of families: 3167
  • Unique surnames: 2375
  • Number of unique media objects: 5909
  • Total size if media objects: 1592 MB

The last number is significant. The vast majority of media objects are jpeg images of scanned source records. As I mentioned before, you can’t have better citations than scans of the original civil and church records.

Cheers! Hans