Happy New Year

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Spending Holidays

Now the Christmas holidays are over and we are waiting for the New Year. Here is the picture of our tree

My sister picked it up from a farmer she knows. Here we actually grow trees to be used at Christmas time. Firs are very common here also in the nature.

We have made an agreement with the family that we don't really exchange gifts. Just something small and this year my gifts were related to Piitu. My daughter had found an artist (Marianne Kokko) who created paintings of dogs from photographs and here she is:

My sister's son has a girl friend who attended Rudolf Steiner school (also known as Waldorf education) like my children and she had made a woollen image of Piitu. It is created with a special kind of felt making using needles. It is not a very known skill nowadays.

I have eaten tons of chocolate and played games with the children. Katri got a game named Toledo for Christmas and I got a Rummikub game from Israel last summer and we have not played it so far. Now we just have to settle an argument about the rules before we can play it again.

I have lots of work planned for the remaining holiday. I should decide which program I am going to teach my students to use in photoshopping. I should also clean my computer folders which are not organized even though I bought the new laptop a year ago. I also should do something to this blog; not to mention my own website which is not even started yet...

Merry Yule

This time of year is important but hard to come up with a suitable wish to all the people over the world. I think before "Seasons Greetings" were very common; now "Happy Holidays" seems to be the correct expression.

Usually I prefer our own "Hyvää Joulua!" and the reason is historic:

Yule or Yule-tide is a winter festival that was initially celebrated by the historical Germanic peoples as a pagan religious festival, though it was later absorbed into, and equated with, the Christian festival of Christmas.The term "Yule" is still used in the Nordic Countries to refer to Christmas. In modern times, Yule is observed as a cultural festival.

Originally the name Giuli signified a 60 day tide beginning at the lunar midwinter of the late Scandinavian Norse and Germanic tribes. The arrival of Juletid thus came to refer to the midwinter celebrations. By the late Viking Age, the Yule celebrations came to specify a great solstitial Midwinter festival that amalgamated the traditions of various midwinter celebrations across Europe, like the solstice celebration. A documented example of this is in 960, when King Håkon of Norway signed into law that Jul was to be celebrated on the night leading into December 25, to align it with the Christian celebrations.

RennyBA has an excellent explanation about this in his blog from the Norwegian point of view.

The explanation of the Finnish tradition in Wikipedia is short and accurate:

On the eve of the Finnish Joulu, children are visited by Joulupukki, a character similar to Santa Claus. The word Joulupukki means "Yule Goat" and probably derives from an old Finnish tradition where people called nuuttipukkis dressed in goat hides circulated in homes after Joulu, eating leftover food. Joulupukki visits people's homes and rides a sleigh pulled by a number of reindeer. He knocks on the front door during Jouluaatto, rather than sneaking in through the chimney at night. When he comes in, his first words are usually "Onkos täällä kilttejä lapsia?",
"Are there (any) good (well-behaved) children here?". Presents are given and opened immediately. He usually wears red, warm clothes and often carries a wooden walking stick. His workshop is in Korvatunturi, Lapland, Finland, rather than at the North Pole like Santa Claus, or in Greenland. He is married to Joulumuori (tr. Mother Yule). Typical Finnish yule dishes include ham, various root vegetable casseroles, beetroot salad, gingerbread and star-shaped plum-filled pastries. Other traditions with a non-Christian yule background include joulukuusi ("Yule spruce") and joulusauna ("yule sauna").

So today is the most important day in Finland. Santa left yesterday and you can even follow the live broadcast at the link on his site. However it does not support Firefox and I am not going to use IE because of that :)

It is early in the morning and others are asleep. I will soon start to make our traditional Rice Porrige, which takes about an hour to get ready.

I think the picture has an excessive amount of butter in it...

I wish merry Yule to everyone!

Mouse Agility

I did not even know mice could be this smart. A long track and he does it on his own!

More about this activity in mouse-agility.com

Dot-A-Pix Example

I will use this as an excercise for my students today. Hopefully I will get enough students for my computer course about image handling and slide shows ;)

If you want to solve this:
The colour of the line is always the colour of the starting point.

Christmas Tree Sudoku

The most popular Christmas tradition wears a new shape this year as Conceptis uncovers a 15-grid Multi Sudoku puzzle with the outline of a Christmas tree.

Unfortunately the poster is not available in Finland but at least I can play the puzzle in Conceptis website. Maybe I should try to e-mail to the publisher in Denmark. They have sent me a couple of Tazuki magazines before.

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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.

Handicraft and Recycling

My daughter and I have had a project which has been going on for at least a month. First of all I love candles. Whenever I see exceptional or beautiful candles I just have to buy them. I never throw the remains away but store them and my daughter has been doing the same. I have not made new candles in several years so we had lots of material collected. Some candles don't burn very well and most of the stearin is left unburned.

I have an old small kettle which I got from my mother and I have used it for melting the stearin for years. Earlier I did not use the right way but I put the kettle straight to the stove. It is actually dangerous if you are not standing right near the kettle with a lid ready. If the stearin gets too hot it can burst into flames.

Now I had to figure out something new. I had bought an induction stove a couple of years ago. Since the wikipedia article shows a totally different picture, you can check the Finnish Helkama here. This type of cooktop does not work with kettles that are constructed from non-conductive materials. Unlike normal electric hotplates an induction cooker creates no heat; only the vessel used for cooking is heated. The basis of heat generation is magnetic field hysteresis loss. So my old kettle did not work any more. Now I used a water bath like I always should have and the vessel next to the stove was made of steel. Like you can see the stove is not heated; I have a towel protecting the stove.

As moulds we used practically everything: Pringles wrappings, energy drink bottles, plastic jam jars and glass bowls which have had candles in them originally.

When the liquid stearin hardens again it loses volume and that is why the candles must be done gradually but that makes the task rewarding. You can see the result when you remove the container. I was totally fed up with the work after one day but my daughter wanted to finish all the materials. These are the ones where the containers were removed by cutting them with a sharp knife.

These are the glass candles

Some people don't want to burn candles but I think candles make the dark winter so much warmer. The Finnish candles are the best. They don't start running, but the extra edges are folded beautifully beside the candle.

Now I have so many candles that I don't have to buy or make new ones in a long time...

Successful Piitu

Last Sunday I was very tired and I felt a little feverish. Piitu was going to attend to her first official agility competition. She had taken part of some competitions "for dummies" but she was dismissed every time because of too many errors. All the obstacles have to be done in a certain order and Piitu usually does not care. I decided to leave home.

This time the coach was Piitu's teacher Noora Salonen who is very experienced in dogs and teaching. Here is a video of the first competition. No mistakes but 3 seconds over the time limit and third place in the competition.

When my daughter phoned us about the success, we decided to go and see this miracle. Maybe because we were there the second track did go wrong from the second obstacle... Result: dismissed. We went back home and Piitu was left for the third competition and this time no errors, not exceeding the time limit and second place. The first step in a hopefully long career. With three similar results Piitu gets to a more advanced level.

Here is the winner with her trophies.

First Snow

Yesterday morning the view from my bedroom window was like this:

It is amazing how much lighter and cleaner the world looks like. The snow is still there after two days and did not melt right away like usual.

It seems that I did not take the picture straight but in fact the trees are leaning to the east. The wind normally blows from the sea and the trees are unable to grow straight.

Never Totally Trust the Navigator

My daughter graduated in May from the University and I had already bought her a book as a gift but somehow it did not seem valuable enough for such an accomplishment. We had very good experiences about navigators on our visit in Israel and we also had several problems travelling to unfamiliar places to dog shows. So I decided that we would buy her a GPS navigator and our choice was Tom Tom which is probably the most popular here even though we had Mio in Israel.

The following story is really embarrassing for both me and my daughter but I decided to tell it anyway. About three weeks ago we were once again leaving for a dog show in Hämeenlinna, about 140 km from here. We have been there often and if we had been wise, we would have used the navigator near the destination. However since the gadget was new, we started to use it from home.

We left very early, about 6 am and it was still a bit dark when we started the journey. The navigator asked if it could include roads with no asphalt and we answered yes. Here it is not a big deal. We have smaller country roads which are not covered. They are not very bad; maybe longer but they don't have so much traffic. That was our second mistake...

The start from home was different than we normally used but since we used the motorway, we thought that there was a link to the main road we normally use. The motorway was definitely the faster option. Then about 25 km from our starting point the navigator started to change our direction. At first all went well, but when the navigator told us to choose a very narrow country road, we were a bit hesitant. Our third mistake...

The road started fine but the longer we drove, the more bumpy the road got. There were rocks on the road and it was so narrow that only one car could drive it at a time. It had been raining a lot in the past days and there was wet clay on the road. By the time we realized we should not have taken that road, we could not really turn back anywhere.

The last thing was a steep downhill towards the river. The middle part of the road was so high that we got totally stuck. At that point the whole road was just clay, no solid part anywhere. Piitu did not make it to the dog show that day. She was not disappointed. She just loved to run around the field near by.

The next thing was to call a tow truck to get us out of there. The most curious thing was that the truck driver did not find us. He said that according to his navigator there is no road there! My daughter walked to the intersection and the truck backed up to us... well almost to us because his truck could not take the last 200 meters.

The truck driver contacted the farmer whose fields were surrounding the road and he came to take a look. He was a bit pissed off but promised to pull us up with his tractor. I can understand his annoyance; he told that we were the third ones he had to save that week (!) because the navigator had told to use that road even though he had several times informed the municipality that the road must get a sign informing that it can't be used. It really was a field road for tractor traffic!

Here is the tractor which saved us. It has the huge plough equipment on the back.

Here the car is finally getting out of trouble:



Safe and even working:

Here is the picture from the Google Maps and it shows the road also. We were stuck at the spot where the red cross is. I heard later that if we had managed to cross the river we probably would not have made it to the Google pointer anyway...the direction we should have followed is the yellow one.

Both of us blamed ourselves for what happened. Well, there is a saying that what doesn't kill you, makes you stronger. The wheels and the bottom of the car have now been washed and the toe has been adjusted.

One of the family members said that maybe this prevented us from facing a far worse accident. Well, we'll never know that :)

Piitu - the Comedian

Now that I finally decided to take the time to update my blog, I noticed that I have not written in a month! This autumn has really gone fast. I have some reasons for missed weekends which I will blog about and my work seems to take so much time. Of course the puzzles take a big part of my time but sometimes I have felt I have not enough time for them either.

Now I decided to show some pictures of Piitu. She is one of the reasons my blogging is suffering. I have gone to so many shows with her and seen agility practises. Sometimes she just arranges shows for us at home. This is one of them. I guess she just got bored and decided to chew her big football to pieces...

I already told Piitu was picking mushrooms with us. Here she is taking good care that the mushrooms will be cleaned properly. Jumping to the kitchen chairs is no problem for her. Actually I have caught her several times climbing to the table...

Piitu really has only two modes, on and off. When she finally gets tired, she totally drops from standing feet. She can really find the most comfortable places to relax.

The last one is a video. Piitu learned to jump into a cardboard box a long time ago. We did not have the box available for a while and when we tried again, she had not forgotten the command, but she really had learned to jump. The jumps were really high regarding the size of the box. We had a good laugh watching.

Piitu's jumping skills are too good. She managed to jump over our backyard fence when she saw Lulu practising on the other side. The fence is 80 cm high and Piitu is very low. I still am wondering if she has acidentally been fed by a cat or something...

Coign of Vantage - addicted again

I think I am much more selective than before, but once again I found a game which got me playing all over again.This is the first screen which shows a hint where the cursor  should be.

The pixels are in 3 dimensions and you have to rotate the image so that you are looking at the picture from above and seeing the projection of the pixels in a plane. It is not very easy at first but the progress makes you scontinue with a new game. One of the good features is that the images are not the same from game to game. It is unbelievable how big the effect on the pixels is when you move the cursor just a little bit.

I found the game in Random Good Stuff and you can play the game here.

Congratulations Ahtisaari

The Norwegian Nobel Committee has decided to award the Nobel Peace
Prize for 2008 to Martti Ahtisaari for his important efforts, on
several continents and over more than three decades, to resolve
international conflicts. These efforts have contributed to a more
peaceful world and to "fraternity between nations" in Alfred
Nobel’s spirit.


Martti Ahtisaari was the President of Finland in 1994-2000.

• In 1989-90 he played a significant part in the establishment of Namibia’s independence
• 2005 he and his organization Crisis Management Initiative (CMI) were
  central to the solution of the complicated Aceh question in Indonesia.
• In 1999 and again in 2005-07, he sought under especially difficult circumstances to find a solution to the conflict in Kosovo.
• In 2008, through the CMI and in cooperation with other institutions,
  Ahtisaari has tried to help find a peaceful conclusion to the problems
  in Iraq.
• He has also made constructive contributions to the resolution of
  conflicts in Northern Ireland, in Central Asia, and on the Horn of
  Africa.
  

He has already been awarded several times:

• 2000: J. William Fulbright Prize for International Understanding
• 2000: Four Freedoms Award
• 2000: Hessen Peace Prize
• 2004: OR Tambo Award
• 2008: Delta Prize for Global Understanding
• 2008: Félix Houphouët-Boigny Peace Prize
• 2008: Nobel Peace Prize

Ahtisaari was the third (or fourth) Finnish person receiving the Nobel Prize

Frans Eemil Sillanpää was awarded the Nobel Prize in Literature
in 1939 "for his deep understanding of his country's peasantry and the
exquisite art with which he has portrayed their way of life and their
relationship with Nature."

Artturi Ilmari Virtanen 1945 in Chemistry for his research and inventions in agricultural and nutrition chemistry, especially for his fodder preservation method.

(Ragnar Arthur Granit was a Finnish scientist who won the Nobel Prize in Physiology or Medicine in 1967 along with Haldan Keffer Hartline and George Wald but he had both Swedish and Finnish citizenship. Granit said that his Nobel prize "belongs fifty-fifty to Finland and Sweden")

Puzzling Safe

I have always been a fan of puzzling items and this one is: Band Saw Safe from portfolio: alex schlegel

The description says:

The 13 drawers of this band-saw box rotate rather than open outward. Objects
for safekeeping are placed into the large, central drawer through a hole in the
bottom of the box. Since the arrows on the front of each drawer point toward
the drawer's open side, objects may be moved from one drawer to another by
first lining up the arrows on the two drawers and then rotating the entire box
so that the objects fall from the first drawer to the second.

I  must admit that if I placed something in safekeeping here, I probably never could get it out myself.

Math Anxiety

I am preparing for a two-day course in learning to use Moodle. Already a year ago I learned about WiZiQ which helps teachers to create online lessons. Browsing their site I found this great presentation about Math Anxiety. It is meant for both teachers and students. I think my conciense about handling the students is clear :)

The presentation is a bit long, but worth to watch.

Mathematics in Noodles

I found this cool video from kottke.org. It is a clip from Philip Morrison's 1987 PBS program "The Ring of Truth: Atoms" featuring chef Kin Jing Mark making noodles to demonstrate the principle of halving.

 

Math Clock

I found the perfect clock in TechEBlog

Probably all people regardless of their math skills can use it, but I really would love to have this in my classroom.

Autumn

This has been a busy autumn. I had good intentions of updating my blog more often but I just have had no time or energy to do that. Even most of the weekends have been busy. I have been in dog shows and picking mushrooms with Piitu, who hopefully will be a good mushroom dog :) She likes to be in the woods and run among the trees but so far she has only found the mushrooms we found first and showed her with the help of some treats.

We had the final national exams for those who graduate high school and grading the papers is never easy, no matter how much practice I have got. The papers are sent to the national student board to be checked again and that is why I have to be careful. I can’t give too good grades because the students will have high expectations and are disappointed when the results come back after two months. I also can’t be too strict because I still hope that my opinion has some value; if I give low points it has to have an effect to the person who checks them after me. We have general guidelines, but they can never give advice to all the possibilities the students come up with.

On top of all this the worst happened again. After less than a year from the Jokela massacre a new one happened in Kauhajoki. The acts are almost identical. Because I am a teacher I have to face the happenings much more closely than most people and there are many issues which disturb me very much.

First of all, I am very sorry for all the victims and their families and friends. I am also sorry for the family of the student who caused all this. Everything I state below is targeted to our society and habits, not any individual.

Last year my son told me that he does not want to talk about the shooting because that was what the shooter wanted, all the “fame” the news give him. I have come to see that my son was even more right than I could ever have imagined. The event was in all the news for weeks and all the newspapers were competing who got to publish the tiniest piece of information first. When thinking about the past year I can remember only two news items going all over the others: Jokela and the foreign minister’s text message discussion!

Maybe it is typical for all humans but I think it is a very typical Finnish way of reacting; the first thing is to find who is to blame! Should the Minister of the interior be fired, did the police make a mistake when they did not take away the gun, why the disturbed young people aren’t treated or even found after Jokela… these are just the top of the iceberg.

A relatively new thing is the crisis control. There are phone numbers to call and all the health centers have to provide help for recovering the crisis. The schools have been advised that teachers have to handle the case in their classes and discuss it with the children (in my case adults). This is something I object to! All people who want to talk about it must be heard and comforted but no one has to face the discussion against their will. There are people like me who want to think things over by themselves first before we want to talk about it.

I have a very vivid imagination; if people are starting those “What if…?” speculations I really can’t handle all the new thoughts I did not manage to create myself. Talking about shooting and disturbed people to young children I condemn totally. Children have the ability of passing things they do not understand. Why make them anxious about things they were not worried in the first place. They will talk if they need to and then the adults have to answer them but on their level. I have argued about this before. I did not allow my daughter to go to the church children’s club when they told me that their subject following the religious calendar was to talk about death and they would read a book titled “Grandfather has passed away”. Why make 5-year old children worried about grandfather dying. My daughter was 25 when it happened and she had time to prepare.

One striking thing last year and now is blaming the whole thing on the internet. YouTube and games are bad for people and also heavy music. My grandmother thought that The Beatles represented all evil and nowadays Beatles songs are taught in schools. The world is developing and there is nothing we can or should do about it. People under 25 years have grown with the computers and know how to use it. The problem is that most of us older people can’t. The only thing we can do is to learn. Then we can advice the children how to act in the cyber space. I have been in a very close relationship with internet over the past year and I know that many of the myths attached to it are completely wrong.

First of all people want to limit the use of YouTube. Well, it is the biggest but how many people know that there are others. A quick Google search lead to a link Top 31 free alternatives to YouTube (video hosting sites). Who knows how many there are altogether.

A common belief is that all contacts to strangers are dangerous. I have found many foreign friends with whom I have discussions through Skype, GTalk or e-mails. The amount of contacts who have tried something suspicious is very small. If I get an e-mail from FBI confirming that a Nigerian bank is reliable and that they need help, I know it is a scam. I also did not believe the announcements I have won the Australian lottery.

The demands for young people are too hard nowadays. I just sometimes wonder if they really are or if the children are too overprotected. There are problems every person has to face at some point of life. We will not be here forever to take care of things but we have to give responsibility for our children.

The most annoying demands are the trends and advices we are given and condemning those who don’t follow them. Do eat healthy, do not smoke, do not drink, exercise at least 1 hour a day. There are strict limits to your weight, curves for the development of children and even small divergence in them creates confusion. I am old enough to ignore advice I don’t want but I really am worried about young people who don’t have enough confidence to know what is best for them. Actually there are not average people even though we all are tried to force to act average.

One exercise I think is the most important seems to be usually ignored. The frase “Mens sana in corpore sano" is usually construed to mean that only a healthy body can produce or sustain a healthy mind but I think it is the opposite way. If you keep your mind healthy you save yourself from physical illness better. Maybe it is too demanding to exercise one’s brain. To me it is the purpose of life, the only way I can keep my mind as healthy as possible. A good puzzle drives anxious thoughts away and when I have no particular worries I use the demanding ones which need my all brain cells. Finishing one gives me positive energy to save for later.

New Online Puzzles

One reason for my slow blog activity has been the new online puzzles on Conceptis website. I have solved both on paper before and loved them but online playing is even more addictive.

Battleships

This is a game I have played as a child with my sister and also taught it to my children. The purpose of playing was to sink the opponent’s ships before my own ships were sunk. This game is played alone and the task is to find the ships with given clues.

From Battleships rules page:

Each Battleship puzzle represents an ocean with a hidden fleet of ships, which may be oriented horizontally or vertically within the grid such that no ship touches another, not even diagonally. The numbers on the right and on the bottom of the grid show how many squares in the corresponding row and column are occupied by ship segments.

Here is a tutorial showing some tactics. The online game is much faster and you can just click on the squares or on the numbers.

If you want to try the puzzles, you can start here.

Hashi

Hashi is also sometimes called bridges. They remind me of planar graphs in graph theory even though solving them does not actually involve mathematics.

From the Hashi rules page:

The object is to connect all islands according to the number of bridges so that there are no more than two bridges in the same direction and there is a continuous path connecting all islands together. Bridges can only be vertical or horizontal and are not allowed to cross islands or other bridges.

Here is the tutorial:



And here you can start playing.

Poland wins 2008 Eurovision Dance Contest!

Congratulations Poland! The best pair won. Finland did not do as well as I had hoped but we won last year....


Marcin Mroczek and Edyta Herbus from Poland won the second Eurovision Dance Contest, which took place tonight in Glasgow, Scotland. Millions of viewers from 21 countries across Europe saw Russia and Ukraine finishing 2nd and 3rd respectively.

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Back To Work

It’s odd how fast time passes sometimes. I have also noticed that the longer the vacation is, the longer you are worried it is going to end soon. The second week in August I started the worrying and thinking about all of the things I had thought of doing during the holidays. Luckily I got over that but many of the things I had planned are still undone.

School started a week ago. The first days are always exciting and I am worried how many students I will have. This year the long mathematics had the greatest success in years. I even had not enough seats in my classroom and had to borrow some from another classroom. That is a really good thing. In autumn, people are starting the studies and make good decisions but later on part of them always drop off, because of work issues, family, … the reasons are numerous.

I had some setbacks also. The most annoying thing is the wireless network. The school computers in the teachers’ lounge were connected to the municipality network and are now protected with passwords. Whatever anyone wants to do, he/she has to log in and remember to log out afterwards. I can’t attach my laptop to the school network but we have a wireless network also. Something has obviously changed at the same time the other network was set up because I am not able to connect anymore. My settings are the same and I tried also with my new cellular, Nokia E90, I bought this summer.

Both the laptop and the cellular found the network but did not connect to the log in page. Now I’ll just have to wait until someone comes and fixes it. Luckily I have a normal computer in my classroom and I can use my USB flash drive if needed.

This week I was really tired and all my time was spent in preparing the classes, the normal things I do on the computer and sleeping! I was so tired that I slept more than in ages. Maybe the bad weather has also something to do with my mood.

Today I found cool cookies. I have blogged about Tetris wallpapers and Sierpinski cookies before, and now fraskedesigns introduced Tetris cookies. I just wonder how to get the colours so bright. My experience with the food coloring is that it shows up different than you intended...

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 :)