Sudoku #55

Category: Sudoku
Sun, 28 Aug 2005, 19:04

It hasn't been long since I started making my puzzles available in a new format. I had expected to post 10 or 20 once every week or so. But today, I just uploaded my 2001st puzzle. If you solve one of these puzzles a day, you now have enough puzzles for five and a half years!

I think it's now time to slow down a bit, and really get back to my original plan. Or perhaps I'll leave it at 2001 puzzles for a while. After all, this is just another silly puzzle.

Hans

path: /Sudoku | permanent link to this entry

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Sudoku #54

Category: Sudoku
Tue, 23 Aug 2005, 21:31

So far, I've put 620 Sudoku puzzles in the Sudoku section of my web site. Today, I added a new feature to the puzzle pages. You can view the puzzles in one of three ways. The default view shows just the puzzle. The "Raw puzzle" view also offers a plain text version of the puzzle. This is suitable for copying and pasting into your own Sudoku solving program. Finally, the "Raw puzzle and answer" view shows all that plus the answer to the puzzle. But I'm sure no one will have to take advantage of that!

Hans

path: /Sudoku | permanent link to this entry

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Sudoku #53

Category: Sudoku
Sat, 20 Aug 2005, 19:03

When generating puzzles randomly by computer program, most puzzles come out looking pretty ordinary. But every now and then a truly marvellous looking puzzle comes out. Have a look at puzzle Advanced 16.1, which I uploaded today. Isn't this an amazing example of what random chance can come up with?

Hans

path: /Sudoku | permanent link to this entry

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Sudoku #52

Category: Sudoku
Fri, 19 Aug 2005, 09:04

For various reasons, I decided to restructure the way I present my Sudoku puzzles. First, the blog format has become a bit unwieldy. Second, it's not that I've run out of things to talk about, but most of what I want to rant on about really belongs in other blog categories. Third, I don't think I can keep up with posting daily, especially now that I'm back to work.

Although I won't be posting puzzles to this blog, I will still create and offer up my Sudoku puzzles. The puzzles I've posted here will now be available at Sudoku, in another section of this website. I've also posted a couple dozen new puzzles that were intended for this blog. I expect to post a page of 10 or 20 new puzzles once a week or so.

Also, I plan on posting some easier puzzles. Or at least, puzzles that don't require any of the advanced solving techniques. I've found that since I enjoy solving the easy puzzles published in the Toronto Star, it seems almost hypocritical to just post challenging puzzles here.

path: /Sudoku | permanent link to this entry

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Sudoku #51

Category: Sudoku
Sun, 14 Aug 2005, 09:39

For Sylvana and me, today is our wedding anniversary. Without a doubt, I can say meeting Sylvana was the best thing that ever happened to me, and I've enjoyed every day of married life.

Some people like to talk about the "traditional definition of marriage". However, there's really no such thing. The institution of marriage has changed constantly over the past centuries, and continues to change. For example, at one time, wives were considered to be the property of their husbands. Fortunately, that point of view no longer exists.

There are other ways marriage has changed. For example, at one time in Ontario, the only weddings that were legally recognized were those performed in Anglican churches. At one time, interracial marriages were illegal, and even dating outside your own race could send you to jail.

For us, marriage could have been difficult a hundred years ago, or in certain other countries, since her family is Catholic and mine is Protestant!

Fortunately, we now live in more enlightened times. And recently, the Canadian government passed legislation allowing even more couples the opportunity to enjoy the institution of marriage.

So, after you're done with todays puzzle, go tell your significant other how much your relationship means to you. On second though, do that first, then solve the puzzle.

Hans

     
  2  
3    
8   3
  6  
5    
6    
  5  
     
5    
  4  
8   2
     
     
     
4   1
  7  
    9
     
  7  
    8
    9
  1  
2   4
    3
  9  
     

path: /Sudoku | permanent link to this entry

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Sudoku #50

Category: Sudoku
Sat, 13 Aug 2005, 08:50

For the 50th posting to this blog, I offer some links to some other (non-Sudoku) web sites that somehow mention the number 50.

Todays puzzle may not be one of the toughest I've posted, but it has a nice symmetrical starting pattern.

Hans

     
6    
5    
     
  5  
1   7
6 3  
     
     
    8
  2  
    4
  9  
7   5
  3  
2    
  4  
8    
     
     
  7 3
4   3
  7  
     
    9
    1
     

path: /Sudoku | permanent link to this entry

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Sudoku #49

Category: Sudoku
Fri, 12 Aug 2005, 07:05

Look carefully at todays puzzle and you might find something a bit unusual. Can't see it? Then before reading any further, start solving it.

Did you figure out yet what's unusual? Look for the number nine in the start values. I got curious, and changed my Sudoku program to generate puzzles without certain given start values. As I suspected, it is possible to have valid puzzles without all digits from one to nine represented in the starting grid.

Is there a minimum number of start values needed for a valid puzzle? I suspect you need eight or nine specific starting values. Consider a puzzle that starts with the seven values from one to seven. As you're solving the puzzle, you'll reach a point where you have some number of unknown cells with the possibilities {8,9}, with nothing further to go on. To have a solvable puzzle, at least one of those cells would have to have either an eight or a nine initially.

As a further test, I told my program to generate a puzzle with two values missing, and it couldn't do it. Mind you, I only gave it a few hours. But that's enough time to generate a couple of thousand puzzles otherwise.

Hans

     
  7  
8    
1   8
     
3    
6    
  2  
     
1    
     
7   5
  6  
7   3
  1  
5   3
     
    4
     
  6  
    4
    1
     
2   7
    8
  4  
     

path: /Sudoku | permanent link to this entry

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Sudoku #48

Category: Sudoku
Thu, 11 Aug 2005, 08:49

This year, I turned 48. You know what, being 48 sucks. Yesterday, I went to St. Michael's Hospital for lithotripsy. If you know what that is, then you know what I had. For the past three weeks, though, while waiting for the procedure, I feel like I've been constantly passing stones. Needless to say, I've been stuck at home feeling pretty crummy.

But one thing that has helped me relax over the past few weeks is Sudoku. Not solving puzzles, but rather playing with my Sudoku program. When I first met Sudoku on the pages of the Toronto Star, it was obvious to me that the puzzle was quite amenable to analysis by computer program. And so I wrote a program. First, I used the programming language Python, which is great for rapid development and prototyping. Later, I rewrote the program in C for better performance.

What also helped keep me sane over the past few weeks was creating and selecting puzzles, writing commentary, and posting them on this blog. Even if no one out there reads my blog or tries to solve my puzzles, this has been very beneficial and therapeutic for me.

Anyways, now that the stone has been successfully obliterated by the great people at St. Mike's, hopefully I'll be back on my feet soon, and I'll get back to more important endeavors, like getting back to work, or finishing the basement renovation job I started months ago. Will that mean fewer Sudoku blog postings? At the moment, I have puzzles ready to go for the next month and a half. All that's needed for most is some commentary. But there's always something to comment on.

Hans

     
     
    6
    3
9    
    4
5   1
     
2 3  
    3
  2  
  5  
8    
     
    2
  7  
  4  
1    
  7 1
     
4   2
6    
    9
7    
4    
     
     

path: /Sudoku | permanent link to this entry

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Sudoku #47

Category: Sudoku
Wed, 10 Aug 2005, 07:06

Today in history, 159 years ago, the Smithsonian Institution was established. The institution came about because of a clause in the will of James Smithson's. It stated that should his nephew, Henry James Hungerford, die without heirs, the Smithson estate would go to the United States of America for establishing an institution "for the increase and diffusion of knowledge among men". At the time, the estate was worth $500,000 ($8,790,303 in 2004 taking inflation into account).

Since then, the United States has become a powerhouse in scientific research and technological development. But that pre-eminent position is under tremendous pressure. Many in the US would like science curriculum to be determined by the government, and not by scientists. More and more these days, scientific policy is being decided by politicians who are poorly trained in science. The result is bad decisions made on the basis of either religious dogma or political ideology.

The science classrooms are considered by some a major battle ground for the hearts and minds of young Americans. Many people stubbornly stick to the naive notion that certain scientific results should not be taught since they think they're contradictory to their religious beliefs. Evolution is a popular target. Some would like "equal time" offered to other ideas, like creationism. Some go so far as dress up creationism in a less religious form and call it "intelligent design". Unfortunately, if you put lipstick and a wig on a pig, it's still a pig.

What's wrong with giving equal time to alternative theories in science classes? There's nothing at all wrong with that idea. Unfortunately, there's nothing scientific about creationism or "intelligent design". Those who advance those points of view offer nothing in the way of scientific evidence to support their theories. In fact, these ideas can't even be formulated into scientific theories at all. One requirement for any scientific theory is that it must be testable. As soon as you consider an "intelligent designer", you're into territory that's simply untestable. If there were an "intelligent designer", you would have to take into account the possibility that the "intelligent designer" could very well interfere with the experiment, rendering any results useless. Alternatively, if you believe that it's possible to design an experiment that the "intelligent designer" could not interfere with, then that would imply that the "intelligent designer" is not omnipotent.

As the "religious right" in the United States flexes its muscles more and more, influencing public policy, there's no doubt at all that the United States' dominent position in science and technology will diminish. This is already happening in certain areas like stem cell research. Another area shaped by political ideology is environmental policy. Important steps needed to stop global warming are not being taken since they might adversely affect the American economy. The long term health of the world is being sacrificed for short term comfort.

Look at this from the point of view of Sudoku. How do you solve a Sudoku puzzle? Do you look for guidance in some holy book? Do you choose a value for a cell based on a majority vote or political ideology? No, you solve the puzzle through a process of logical deduction. If logic is so important to such a silly game, why isn't it important enough when considering education and public policy issues?

Hans

8    
     
4   1
     
9   3
    7
    5
     
2    
  1 7
     
3 2  
     
     
     
  5 2
     
6 8  
    4
     
1    
8    
6   5
     
9   1
     
    7

path: /Sudoku | permanent link to this entry

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Sudoku #46

Category: Sudoku
Tue, 09 Aug 2005, 07:59

1. God is our refuge and strength, a very present help in trouble.
2. Therefore will not we fear, though the earth be removed, and though the mountains be carried into the midst of the sea;
3. Though the waters thereof roar and be troubled, though the mountains shake with the swelling thereof. Selah.
4. There is a river, the streams whereof shall make glad the city of God, the holy place of the tabernacles of the most High.
5. God is in the midst of her; she shall not be moved: God shall help her, and that right early.
6. The heathen raged, the kingdoms were moved: he uttered his voice, the earth melted.
7. The Lord of hosts is with us; the God of Jacob is our refuge. Selah.
8. Come, behold the works of the Lord, what desolations he hath made in the earth.
9. He maketh wars to cease unto the end of the earth; he breaketh the bow, and cutteth the spear in sunder; he burneth the chariot in the fire.
10. Be still, and know that I am God: I will be exalted among the heathen, I will be exalted in the earth.
11. The Lord of hosts is with us; the God of Jacob is our refuge. Selah.

The above is Psalm 46 from the King James Version of the Bible.

Was William Shakespeare involved in the writing of the KJV? Did he surreptitiously insert a clue into Psalm 46? Note that the 46th word of Psalm 46 is "shake", and the 46th word counting backwards (not counting the closing Selah) is "spear". Also note that Shakespeare was 46 when the KJV was completed in 1610.

Most experts on both the Bible and Shakespeare will tell you there's no evidence at all that Shakespeare had anything to do with the KJV. Statisticians will tell you that it's not at all difficult to find such coincidences. But still, such coincidences can be fun to speculate about.

Hans

  7  
     
1   8
6    
    3
     
     
    8
2    
    6
     
4 2 3
  9  
     
  5  
5 1 4
     
8    
    4
2    
     
     
5    
    8
9   7
     
  3  

path: /Sudoku | permanent link to this entry

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Sudoku #45

Category: Sudoku
Mon, 08 Aug 2005, 11:16

I don't look at the night sky often because of the light pollution here. But one evening this past winter I went outside with our binoculars looking for the comet that was visible to the north. It wasn't easy, but I eventually found it. Afterwards, I turned the binoculars to a couple of other easier to find things, such as Orion's belt and sword, and the spectacular open star cluster, the Pleiades.

Astronomer Charles Messier assigned the number 45 to the Pleiades while compiling his list of "fuzzy" objects (nebulae) in the sky. Known since ancient times, the Pleiades consists of at least 500 stars spread over 2 degrees in the sky. At least half a dozen are visible with the naked eye, but under ideal conditions, more than a dozen can be seen.

The cluster is also known by other names besides M45. It's also known as the "Seven Sisters" following Greek mythology. The parents are called Atlas and Pleione, and their seven daughters are Alcyone, Asterope, Electra, Maia, Merope, Taygeta and Celaeno. In Japanese, the cluster is known as Subaru, which also inspired the name of a automobile company. In Persia, it was called Soraya.

Hans

1   9
     
     
    2
7    
4   8
    3
    1
5    
     
6    
  9 4
     
     
     
3 1  
    5
     
    8
7    
5    
2   4
    6
9    
     
     
4   2

path: /Sudoku | permanent link to this entry

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Sudoku #44

Category: Sudoku
Sun, 07 Aug 2005, 09:24

Stephen Harper, leader of the Conservative (Reform Alliance) Party, was in Toronto promising to make the cost of transit passes tax-deductible. This is one nice promise that would help out many who use public transit. But it's only one thing. Transit systems in Ontario, like the TTC, are hurting bad these days, and the best thing that would help them is simply more money. Don't forget that the Conservatives voted against the last federal budget that included investing $800,000,000 in public transit!

Harper's got a long long way to go if he wants to make inroads in Toronto. We Torontonians have a long memory. We remember full well what Mike Harris did to the TTC's expansion plans back in 1995. We have no reason to expect anything different from any federal Conservative. Especially Conservatives cut from the same cloth. We know full well that tax breaks don't help public transit. Funding does.

By the way, I've created a new e-mail address specifically for my Sudoku related mail. Click on the "Send e-mail" link at the left if you want to e-mail me on anything Sudoku related, or anything else related to what you read here in this blog.

Hans

  6  
2   9
     
     
  3  
    8
    5
    8
    7
  2  
1    
  4  
     
4   6
     
  8  
    9
  1  
5    
7    
6    
9    
  2  
     
     
5   3
  7  

path: /Sudoku | permanent link to this entry

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Sudoku #43

Category: Sudoku
Sat, 06 Aug 2005, 08:35

On this day in 1806, the Holy Roman Empire dissolved as its last emperor, Franz II, abdicated. The Holy Roman Empire was a more or less loose conglomeration of various kingdoms, principalities, grand duchys, duchys, etc. spanning much of central Europe. After the Peace of Westphalia in 1648, which ended the Thirty Years War, the empire had become pretty much meaningless anyways. Voltaire described the Holy Roman Empire as "neither Holy, nor Roman, nor an Empire".

On this day in 1945, an American B-29 bomber nicknamed Enola Gay dropped an atomic bomb on the Japanese city of Hiroshima. Eventually, about 200,000 people would die, either from the initial blast, or from radiation sickness. In the 60 years since, the United States remains the only country to have actually used nuclear weapons against an enemy.

On this day in 1984, Prince (AKA Prince Roger Nelson) released his album "Purple Rain", launching him into superstardom. What some might not know is that Prince has a home in Toronto's Bridle Path neighborhood, an enclave of mansions housing many of Toronto's nouveau riche.

On this day in 2005, Sudoku puzzle #43 was posted in the Boldts' Omnifarium weblog.

Hans

     
8 6  
     
    5
    9
3   7
     
  2  
4    
7 8  
2    
4    
     
     
     
    5
    6
  8 3
    8
  5  
     
9   4
7    
5    
     
  1 9
     

path: /Sudoku | permanent link to this entry

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Sudoku #42

Category: Sudoku
Fri, 05 Aug 2005, 10:17

As most of you already know, 42 is the answer to the great question of life, the universe, and everything. But of course, although we know the answer, no one is quite sure what the question really is!

The five volume Hitchhikers Guide to the Galaxy trilogy (by Douglas Adams) is very much a part of the consciousness of the members of my generation. For some reason, this is especially true amongst computer professionals and hobbyists. For example, the "Babel Fish" inspired the name of one particular translation web site. The number 42 may well be one of the more ubiquitous concepts from the trilogy, representing some profound truth that nobody really understands.

Todays puzzle is nicely balanced. It's not only symmetric, but every group (row, column, square) has either two or three seed values.

Hans

7    
     
8   9
  2  
4    
    7
  5  
  2  
     
  5 1
     
4    
     
7   6
     
    2
     
9 8  
     
  4  
  8  
3    
    9
  1  
8   4
     
    6

path: /Sudoku | permanent link to this entry

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Sudoku #41

Category: Sudoku
Thu, 04 Aug 2005, 11:10

When a superior person hears of the Tao,
She diligently puts it into practice.
When an average person hears of the Tao,
he believes half of it, and doubts the other half.
When a foolish person hears of the Tao,
he laughs out loud at the very idea.
If he didn't laugh,
it wouldn't be the Tao.

Thus it is said:
The brightness of the Tao seems like darkness,
the advancement of the Tao seems like retreat,
the level path seems rough,
the superior path seem empty,
the pure seems to be tarnished,
and true virtue doesn't seem to be enough.
The virtue of caution seems like cowardice,
the pure seems to be polluted,
the true square seems to have no corners,
the best vessels take the most time to finish,
the greatest sounds cannot be heard,
and the greatest image has no form.

The Tao hides in the unnamed,
Yet it alone nourishes and completes all things.

The above is Chapter 41 of the Tao Te Ching. The Tao Te Ching was written about 2600 years ago in China, and attributed to the philosopher Lao Tzu, considered to be the founder of Taoism.

As I said yesterday, I've been playing with puzzles with four-fold symmetry. Here's a puzzle with four-fold reflectional symmetry about the two diagonals.

Hans

    6
     
2    
4   2
    1
8    
     
9    
  5  
4   9
     
6 3  
     
     
     
  2 3
     
1   7
  9  
    5
     
    7
6    
9   3
    5
     
8    

path: /Sudoku | permanent link to this entry

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Sudoku #40

Category: Sudoku
Wed, 03 Aug 2005, 09:19

First, for those who landed yesterday on Air France flight 358, welcome to Toronto!

During the past weekend, I added some improvements to my Sudoku program to generate puzzles with four-fold symmetry. There are several ways to have puzzles with four-fold symmetry. The first is four-fold rotational symmetry. That is, a puzzle that has the same pattern when rotated 90, 180, or 270 degrees.

There are also a couple of varieties of four-fold mirror symmetry. One type is reflection about both the horizontal and the vertical. Another is reflection about the two diagonals.

Of these types of symmetry, generating puzzles with four-fold rotational symmetry seems the fastest, with puzzles generated only a bit slower than with two-fold rotation symmetry. Mirror symmetry about the two diagonals is slower, and about the vertical and horizontal much slower still.

Todays puzzle features four-fold rotational symmetry. I rather like the appearance of this type of symmetry, so I may be doing more of this style of puzzle.

Hans

2   7
     
  1  
  9  
     
    2
    3
1    
    4
    3
5    
     
6   7
     
8   9
     
    6
4    
3    
    8
7    
2    
     
  4  
  8  
     
9   2

path: /Sudoku | permanent link to this entry

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Sudoku #39

Category: Sudoku
Tue, 02 Aug 2005, 09:18

Here's what David Wells has to say about the number 39 in The Penguin Dictionary of Curious and Interesting Numbers:

"This appears to be the first uninteresting number, which of course makes it an especially interesting number, because it is the smallest number to have the property of being uninteresting. It is therefore also the first number to be simultaneously interesting and uninteresting."

Sudoku puzzles use the numbers from one to nine, each of which is considered "interesting". The number one represents unity. Two is the only even prime number. Three is common in religion and mythology. For example, the trinity is an important concept to many Christians. Four is the maximum number of colors needed to color a map.

Five is the number of fingers on one hand. Five is especially interesting - Wells devotes nine pages to it! Six is the first "perfect number" since 6=1+2+3 and 6=1*2*3. Seven is the number of days in a week and the number of deadly sins. Eight is the second cube and the only cube that is one less than a square. Nine is the third square and the number of people on a baseball team.

Anyways, I hope you find todays Sudoku puzzle interesting!

Hans

  5 3
     
     
    4
3    
  9  
  9  
    2
    6
    2
     
    7
8 5  
     
  3 6
1    
     
5    
8    
6    
  1  
  4  
    7
6    
     
     
8 4  

path: /Sudoku | permanent link to this entry

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Sudoku #38

Category: Sudoku
Mon, 01 Aug 2005, 09:52

Today is a holiday for most Canadians. For those who want to spend the day relaxing with puzzles, here are enough Sudoku puzzles to keep you busy for the day.

Hans

a)

    2
     
  8 4
6    
5   3
1    
     
9    
  2  
9    
1    
    6
     
     
     
7    
    3
    5
  6  
    5
     
    1
4   9
    5
5 3  
     
8    

b)

  2 5
7    
4    
    1
     
6    
    4
     
  5  
  3  
    8
     
  9  
2   7
  4  
     
1    
  3  
  1  
     
5    
    8
     
4    
    3
    8
2 1  

c)

  4 5
     
     
2   9
  7 8
     
     
3    
2    
     
1 6  
9   2
     
     
     
8   6
  9 5
     
    4
    7
     
     
1 2  
4   5
     
     
1 6  

d)

3 2  
7    
     
  6  
3   9
    7
  1  
     
  4  
1    
  9 6
     
     
     
     
     
8 7  
    3
  4  
     
  7  
5    
6   4
  8  
     
    2
  9 6

e)

  4  
     
3    
    2
    8
5 6  
3    
    1
     
1   6
     
5   9
     
     
     
7   2
     
6   3
     
4    
    5
  9 6
7    
3    
    8
     
  9  

f)

  2  
    3
     
  9 5
     
    3
  6  
1    
5    
    2
     
  9  
  4 9
     
8 7  
  5  
     
3    
    5
    4
  6  
1    
     
2 3  
     
8    
  7  

g)

     
2    
    8
8   6
  4  
     
3    
    5
     
     
9   4
  8 7
    5
     
6    
6 7  
5   1
     
     
1    
    2
     
  2  
7   9
1    
    8
     

path: /Sudoku | permanent link to this entry

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