Make Puzzles Not War

I have often imagined what would have happened if mathematics concepts could be copyrighted. Newton developed differentiation and integration to complete his gravitational theory. What if he had realized that the idea is very valuable and had copyrighted it? All the other scientists would have had to use other methods for various problems or had to pay Newton to use it. Science would not have developed. Pure mathematics is actually a theory of different methods and the applications are used by physicists, economists, chemists, biologists and so forth. All intellectual development had suffered. In this case Leibniz was working on the same problem at the same time and there would have been a huge argument who actually got the original idea.

Luckily ideas can not be copyrighted. In the scientific world mathematicians publish their work for the benefit of everybody. When someone creates just a problem he may get his name in history like Fermat in Fermat’s Last Theorem. Andrew Wiles has now proved the theorem but it just may happen that someone will create a much better proof and Wiles will be forgotten. Mathematics strives for the best solution and the person who provides that, gets his/her name in history.

KenKen, CalcuDoku, Square Wisdom or Mathdoku?

KenKen is a mathematical puzzle. The goal of each puzzle is to fill a grid with digits so that no digit appears more than once in any row or column. Grids range in size from 3x3 to 9x9. Additionally, KenKen grids are divided into heavily outlined groups of cells and the numbers in the cells of each group must produce a certain given number when combined using a specified mathematical operation (either addition, subtraction, multiplication or division).

The image above is not a KenKen puzzle, it is Calcudoku. KenKen is now a registered Trademark of Nextoy, LLC (as well as KenDoku) and the books containing KenKen’s are authored by Tetsuya Miyamoto, and Will Shortz; Kendoku books are authored by by David Levy and Robert Fuhrer; Dj Ape used originally the title Square Wisdom; The Puzzle Society uses the name Sukendo; The Kindle version is Mathdoku and the puzzle above is a Conceptis made Calcudoku, which name is also used by Dj Ape in the later books. The trademark does not prevent people from doing similar puzzles, it just prevents others calling them with the same name.

The abundance of different names is confusing for the general public and makes it more difficult to assess the overall popularity of the puzzle. When the Sudoku popularity was at the highest, we had many different Sudoku books and magazines available in Finland made by local puzzle makers. Now we don’t have a single KenKen (or Calcudoku) book available. If all those puzzles had the same name people would find them better and the mathematical challenge could find also people who are not puzzle addicts like me. I constantly meet mathematics teachers who never have heard of these puzzles. It will never reach the popularity of Sudoku.

Variants of Sudoku

Actually KenKen is also one form of sudoku. It is also based on a Latin Square which is an nxn table filled with n different symbols in such a way that each symbol occurs exactly once in each row and exactly once in each column.

Here are 2 examples of 5x5 Latin squares.

Sudoku is a Latin square with an additional rule: The objective is to fill a 9?9 grid so that each column, each row, and each of the nine 3?3 boxes (also called blocks or regions) contains the digits from 1 to 9 only one time each. The puzzle setter provides a partially completed grid.

This puzzle is known to most people, because it became very popular and newspapers publish them daily even though the biggest boom is over. The amount of different Sudoku answers is of course smaller than that of 9x9 Latin Squares because of the 3x3 box rule. The amount of puzzles is bigger and depends on the givens, the numbers provided on the puzzle.

(For those who are interested on the mathematical calculations about the amount of Sudoku’s or the minimal amount of givens, I recommend the Wikipedia article on Mathematics of Sudoku. It contains links to several mathematical articles about the subject.)

Colour Sudoku

The classical Sudoku has the 3x3 boxes. The third rule can however be obtained in many ways and these puzzles are called Sudoku variants. Different lists of them can be found all over the internet. Some of the variants have made it to publications containing these variants; some of them are published regularly on Sudoku variants magazines, some others have been created just for examples. The longest list I found is made by Uwe Wiedemann.

One not so know variant is Colour-Sudoku. This example is from Added Bytes.

Here the third rule comes from the colours; every colour represents the “region” which has to contain each number only once. Here the region is totally spread all over the grid. The size would not have to be 9x9. The same arrangement could be obtained by any nxn grid.

Now Conceptispuzzles has published a new variation called Chain Sudoku. The release article got a very angry response from Strimko. Their puzzles have the same idea; the third rule defining the region is obtained by lines connecting the numbers. This variant has also different sizes. Here is an example of Conceptis Chain Sudoku.

Battle

Now Strimko says that the intellectual idea belongs to them. In some comments they also claim that the streams have not existed before and this idea is totally different from Irregular Sudoku.

Here is an irregular Sudoku, and this would make a Chain Sudoku very easily:

The Chain Sudoku contains one feature which irregular Sudoku doesn’t, the ability to link numbers diagonally.

However this is not a new idea even for Conceptis. In August 2006 Sterling published a book Snakes on a Sudoku – official Snakes on a Plane Puzzle Book and the puzzles were created by Conceptis. Here is one scan from the book:

As you can see there is also the diagonal snake. Somehow the word stream describes these better than the previous ones. To me they look chains. The logic I use in solving both types is the same!

Mathematically speaking

I have also seen a more advanced approach to connecting the numbers, a Toroidal Sudoku:

In mathematics toroid is the doughnut-shaped object. These puzzles are scanned from a magazine BBC Mind Games Christmas 2006. This could really be clued to make a doughnut, but I think it’s better to solve it first. Dr Gareth Moore publishes these regularly on his Puzzlemix website.

Mathematically speaking Strimko’s and Chain Sudoku’s are graphs, more precisely they consist of connected acyclic graphs which are called trees. An acyclic graph with multiple connected components is sometimes can be called a forest.

There is also another puzzle closely connected to graph theory: Hashi. The rules in Hashis are however totally different

As a conclusion to the above; any puzzle having the third rule in addition to the row/column –rule is just another variation in the Sudoku family. Conceptis has an algorithm to create Sudoku’s and Dave Green states in Conceptis Forums:

“To demonstrate how close these puzzles behave, it took us only several minutes to modify the algorithm and the graphical export of our Sudoku generator to enable it to produce Chain Sudoku puzzles.”

I have done some programming but my main interest is algorithms in general and I know that if the code is written using good programming, the changes are easy.

I think I answered this question.

Gareth Moore's Colour Sudoku

There is still the design, but even there Strimko is not totally original. Here is another Sudoku from Gareth Moore which uses colours instead of numbers:

My love of logical puzzles started originally from my main interest, mathematics. I think logical puzzles are very good in learning logical thinking which is a very important skill in mathematics. Puzzles are not as threatening to students as mathematics sometimes seems to be. To me it is a very sad thing that copyright issues get in the way of making these puzzles publicly known. Sudoku’s became popular because the Japanese puzzle company Nikoli, which created the name Sudoku, never trademarked it outside Japan. (Nikoli did not invent the puzzle).

Crediting Strimko

Some of the comments have been criticizing that Conceptis does not give the credit to Strimko. With all the puzzle types Conceptis has provided info about the history of the particular puzzle and I have no doubt they would have made it this time also but quoting Serhiy Grabarchuk in Conceptis Forums:

"Some months ago I warned Conceptis Puzzles that if they will use the idea of Strimko (under any name) with the same features as our Strimko, we will understand that as a direct and clear infringement of our intellectual property rights."

I hope there will be some solution to this. I wrote my opinion to my blog because I see no point in joining all the puzzling forums Strimko has left their accusations. Those who are interested in them can use Google to find them. If Conceptis decides to drop out this puzzle, I will not solve them. I want to find my puzzles on the same website. I have too many links to various social media sites and educational sites as it is!

Relaxing Holiday

I was on holiday. Despite my decision in the beginning of the summer vacation I just had to go to Israel for one week. The trip was too short but the feeling to be away from home made me wonders. My mind was totally reset from the past school year and even after I came home I have been able to relax instead of worrying all the things I should be doing at the moment.

At home I have spent the days in my social networks but mostly I have enjoyed my puzzles. Nowadays my main interest is Pic-A-Pix. Here are 4 screen shots of last week's 6 puzzles.

This week all the others are back to work and I am spending my days with Piitu. I should really start planning next year but as it seems I am not making very good progress. Sometimes I hope I had a job I could leave outside my home. This way it seems I am at my workplace all the time...

Solving a Conceptis Color Pic-a-Pix Puzzle

I think I have spent too long blogging about other things but finally I got into recording a session about solving my favourite type of Conceptis puzzles, a color Pic-a-Pix. These I prefer solving on the computer because I always have trouble finding the right color pencils even though my house is basically filled with ones my children got from school and left behind when they moved away. The other problem is that color pencils are much more difficult to erase than regular pencils.

This particular puzzle can be found here along with other similar bigger puzzles. Because this is a very easy puzzle, I could solve each colour on its own. With harder puzzles that solving method is either impossible or at least makes solving the puzzle even harder.

Notice that you can watch the video on full screen. I made it with ScreenToaster which is an excellent tool for recording your screen. The video is stored on the website and you don't have to upload any software on your computer.

Capture your screen in seconds

Benefits of Vacation

Now that I have no obligations regarding work, I don't have to feel guilty about solving puzzles. My favourite puzzles are Pic-A-Pix and that is why even these six were not enough for this week.

The next one in line was Fill-A-Pix, but they were not very big this week

So I had to turn to the Link-A-Pix puzzles which normally are too easy for me. There was this one MegaLAP and I thought I would solve it. After solving that I remembered how nice pictures they have and decided to try some more and as I went backwards from the biggest to the smallest, I noticed that I still had time for more... ending up solving them all before the new update.

Here is a better screen shot of the bigger ones

Now that I have finished this Conceptis should have updated the puzzles and I can start solving a whole new set,

Fun Searching with Spezify

From the mathematics point of view I have been very thrilled with the new search engine, WolframAlpha. I just wrote some basics about it in my Finnish blog. Then miraculously I found a totally different search engine yesterday named spezify. It is still in beta and to my surprise located in Sweden.

Here is part of my search for "japanese logic puzzles". As you can see the results are shown visually. The results contain Twitter messages and for some reason Conceptis was very well represented. Someone called the results messy but I liked it in some weird way. I had the urge to click and check the results and with Google I try to avoid clicking any extra links. Browsing the results was hard in the beginning using the mouse, but when I realized the arrow keys work the best I had fun!

Before opening a link you can check where it came from. One click on the picture gives black frames with the basic info.

The results with even Finnish search words are mostly in English.
Now I have to start playing with the mathematics links. So many fantastic looking pages!

Teaching Mathematics in Finland With Japanese Puzzles

This is a repost from March for educational purposes with some pictures added here.



In the end of 2008 I had the chance to teach Japanese puzzles in my own school. Now my story has been published on Conceptis website :) I hope this gives ideas to other mathematics teachers as well. Some puzzles in the middle of normal work is refreshing and teaches logic reasoning. Logic is the foundation where mathematical thinking is built. I hope you enjoy the story.



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The Satisfaction of a Solved Puzzle

In February when my holiday started, I took a huge challenge to solve a 110x175 Pic-A-Pix puzzle. It was not as hard as I had imagined but it took a great deal of my holiday. I am not complaining; those hours were very enjoyable. I almost got it finished before the end of the holiday but I got affected by the most common problem, miscalculation in some clue. I erased the area in the centre probably 5 times, always getting a little bigger part right. At that point I was ready to take a break from it, but said to my daughter that she could solve it if she wanted to, and she did! The wrong block had appeared actually very early and that is why I had not got it fixed. I should have gone a bit lower. Now the colouring of the puzzle has taken longer than the solution. I finished it last night watching who won the Survivor China. Here it is (the darker areas on the background are mostly shadows...):

The fantastic thing about this puzzle was all the detail. It made solving interesting and the result very lively.

Now my husband says that I have to frame it and hang it on the wall. That is something I just can't do. It has a 175x110 puzzle on the other side...

Related posts: Skiing Holiday With a Puzzle

Skiing Holiday With a Puzzle

I really have been neglecting my blog! One of the reasons has been my work and the computer classes. I have a new Finnish blog Kompuutteri about computers and updating that for the students has taken me more time than I ever would have expected. Explaining programs and Internet as clearly as possible is not as easy as it may sound. Things I consider matter-of-course can be totally unknown to someone else.

Now I am having my skiing holiday. It has been a tradition in the Finnish school system as long as I have been involved, either as a student or a teacher. We don't really have skiing conditions here in the south by the sea but I prefer the old name instead of just a winter holiday which is used nowadays.

I had very many good intentions about my blogs and cleaning the computer files as well as cleaning the house but I needed some relaxation after the tiresome week in school. I subscribe to a couple of Japanese magazine and the latest issue of Logic Paradise had a huge 110 x 175 Pic-A-Pix included. I decided to give it a try:

After the first day I had some progress to keep my spirits up:


There were mental distractions as well as physical :) Piitu is actually an experienced solver. I have a picture of her solving a puzzle with me when she was a couple of months old.


After two days I was confident I would manage it:


And then I was hooked! I had to take breaks but soon my mind started to wander back to the puzzle and there I was, solving the puzzle forgetting all about the other things I should have done. The totally white spaces in the picture are reflections from the flash light. The paper is glossy and the it is not straight any more. At certain angles all the light reflects back.

As you can see I have made some attempts on the right by counting the overlaps but they did not get me very far. The solution advances along the picture. At some points when I have thought I was stuck, the next step was found after a break with a clear mind. There have always been clues which I just did not notice the first time.

Even though I have not followed my original to-do-list I feel so relaxed and happy. This is something I could do all the time.

Games - Good or Bad?

This week Oxford University reseachers revealed that Tetris can actually be a treatment to traumatic stress.

Players had fewer "flashbacks", perhaps because it helped disrupt the laying down of memories, said the scientists.

It is hoped the study could aid the development of new strategies for minimising the impact of trauma.

I can agree on the part that games which keep the mind occupied are good for any stress but I would not really give all the credit to Tetris. Tetris happens to be the game which started the evolution of puzzling games but at least for me it would not work any more. I played it almost 20 years ago so much that I could not bother to play it again.

To me japanese puzzles have the same effect. I managed to cope with my father's death and other stressful things playing puzzles and choosing the difficulty level according my ability to concentrate. Trying to solve too hard puzzles may have the opposite effect.

A survey conducted 2006 by Psychologist Dr. Carl Arinoldo even suggests that games can relieve pain. (link via cultcase)

88% of players indicated they experienced stress relief from playing casual games and 74% cited mental exercise as a benefit; when asked to choose the most important reasons for playing, 41% picked "stress relief/relaxation," more than twice the number (19%) who chose "entertainment"; 27% said the games provided distraction from chronic pain and/or fatigue, and fully 8% said they derived actual relief from chronic pain and/or fatigue.

Several scientists, like Dr. David Walsh have recently claimed that internet and gaming can be an addiction

Other things in their life get neglected, sometimes even their health gets neglected, their grades start to suffer, relationships start to suffer, and so it starts to bear all the behavioral hallmarks of an addiction. And so I think that’s why the term has emerged.

There are even places where people are treated because of this addiction like The Smith & Jones Centre in Amsterdam.

Using traditional abstinence-based treatment models the clinic has had very high success rates treating people who also show other addictive behaviours such as drug taking and excessive drinking.

But Mr Bakker believes that this kind of cross-addiction affects only 10% of gamers. For the other 90% who may spend four hours a day or more playing games such as World of Warcraft, he no longer thinks addiction counselling is the way to treat these people. "In most cases of compulsive gaming, it is not addiction and in that case, the solution lies elsewhere."

Seems a bit controversial to me. In logic this is called circular reasoning.

Puzzle Heaven

The flu does not seem to leave me alone. Sunday night I started coughing and woke up all the time. I slept most of Monday and Tuesday having also a headache. I had my Japanese puzzles course on Tuesday and I should have done lots of other things while the students were solving their puzzles, but I started to do the Mega-Pic-A-Pix on the Conceptis weekly puzzles. I had an amazing recovery or maybe I just forgot I even had a flu. Working with that puzzle and neglecting my other activities I finally finished it two days later on the same puzzle course :)

Here is a snapshot of the amazing picture:

This is bit blurry, but now it is on the 3 meters wide white screen in front of the class. I just had to show it to the students :)



Nowadays My Conceptis page looks like this. I solved some sudokus also, but I did not solve the first one and that is why it is empty.

After solving the Mega puzzle I just had to do the last black and white puzzle to get the page full. This was the first week Conceptis had 6 weekly PAPs. One was my favourite, the 2-colour puzzle. From now on the weekly treat will be 6 puzzles with one 2-colour PAP and one Mega about once a month ;)

I also took a snapshot of the Link-A-Pixes. The pictures are so beautiful! One was left unsolved.

New puzzles were published today. Now I have a new set and also the weekly review puzzle is a PAP. I think I am able to finish that one tomorrow to be able to review it.

A Starter's Guide to Japanese Pic-A-Pix Puzzles

I have very often written about my favourite Japanese puzzles, Pic-A-Pix –puzzles, like Conceptispuzzles has named them. Other names for these puzzles are also used. However I have never adviced how to solve them. A new techniques article was published in Conceptispuzzles website last week. The problem with these puzzles is that the solving methods can vary very much and people can use their own logic in solving. I decided to show my technique with the same puzzle which is used in the article. I also want to point out that solving can always be done by logic. No quessing is needed and usually ends up in a mess!

The bigger puzzle above and almost the same as this smaller one can be played online on Conceptispuzzles website

The empty grid consists of rows and columns. Both have numbers which show how many black squares have to be painted on the respective row/column. The row 5 has clues 3 4 which means that on that row you will have to paint 3 consecutive squares and 4 consecutive squares but these two blocks are separate.

Well, that should be easy. The problem here is that the painted squares have to fit both the row clues and the column clues. A valid puzzle has only one solution matching those clues and that is why it is important to think which ones have to be painted and which remain empty.

The result of the painted squares is a picture. Sometimes you can even tell that something is going wrong when it looks like a person’s eye seems to be shifted near his ear. Sometimes you can’t conclude what the picture will be until you have solved it all.

Usually I check first the edges. This puzzle definitely has better places to start, but these instances are generally very rare. If none of the edges can be used, I try to find the best row or column as near the edge as possible. Keeping close to the edge is safer and easier for the starting solvers. I still use it as much as I can in big puzzles. It makes me able to check the row/column clues more often.

In the future I use the word clue when I am referring to the given number on the top or on the right. The painted squares and painted blocks are the visual representations of these clues in the puzzle.

In this puzzle three of the edges are impossible to start with. There is no way to tell where 1; 2; or 1,1 should be put in the grid. The bottom edge has clue 7 and I could use that, but the clue 10 two rows up is even better. It fills the whole row.

Now I will check what that means regarding the columns. Column a has only clue 1 and I have painted one. I’ll mark all the others done.

Column b has clue 2 at the bottom. I can’t place it starting from the bottom. If I would, I had a block of 3! That means the bottom square to be empty. Any other conclusions I cannot make at this point.

Column c has clue 3 at the bottom and I can’t conclude anything (actually I could but that is more advanced).

Column d has clue 10 and so does h. I can fill them all. In between the columns all have clues 3 and I will leave them like in column c.

Column i has again clue 3 and is left alone.

Column j is interesting. I can make the same conclusion as in b. The block 2 does not reach the bottom. I can also make the conclusion that it can reach only one square upwards. I can delete all the other squares. This is the advantage of rows/columns with only one clue. When you find it, you can exclude squares.

Now that I have checked all the columns, I will go back to rows and start from the bottom. Row 10 has only left 7 squares so I can paint them all and row 9 has left the nine squares and can also be painted.

Now I could go on with the rows, but now the edge is ready. I will go back to the columns and I can see that all the bottom clues are painted. I’ll mark the squares above them because there has to be empty before the other blocks can continue.

I could have done this before but this is the point where I finally have to do it. I mark all the clues I have used and checked.

Back to row 6. Since the right side is nearer the edge I’ll start there. To the right I need a block of 4 and the second square is black. At this point I can’t be sure of the first one, but the third and fourth have to be black.

Ahaa! I can’t paint the fifth because it would be attached to the next one and I would have a block of 5. So the first square was also black and I can mark the fifth square empty.

Now the row has left 3 squares which have to be black. Row 5 is exactly the same as row 6 was.

Row 4 has two one’s and they are there. I can mark all the others empty.

But wait, I have more blocks finished in the columns and now I can check if they match the clues.

Everything is OK, I can mark the 2’s as finished and at the same time I notice that columns b and f are ready.

Now rows 3 and 2 can be painted. There is only one way to get the 3-blocks fit. Row 1 is already finished!

Now the last thing is to check that the column clues agree on the blocks. Everything is fine and the picture is finished.

Sometimes in small puzzles you have a hard time trying to figure out what the picture is supposed to be. In these cases you should look at the picture from very far (or resize it on your computer).

This was easy to see from the big picture but the tiny one is definitely clearer.

Next time I will try to explain solving coloured PAPs. Meanwhile you can try to solve the small PAP on my sidebar :)