Wednesday, August 20, 2008

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 :)
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