## 20 March 2019

### Nonogram / Picross Tricks

I occasionally play Nonograms or Picrosses depending on however you like to call them. They're as enjoyable as Sudoku if not more. After a while, you may or may not figure out some tricks to help you solve the puzzles faster. Today I'm gonna share my tricks with you.

### Reminder: What Is Picross / Nonogram?

Nonogram also is known as Picross is a number puzzle that gives you mostly an empty grid with numbers on top and on the very left. These numbers work as hints. The number that's to the very left of the row gives you the number of fields that should be marked in this line. The numbers depend on the size of the puzzle. Usually, the puzzles have sizes of five to 15. As such the hint numbers are also from zero to 15, where zero means no fields should be marked. Additionally, the numbers only mark adjacent fields and if multiple ones mean they're spaced, as in they have one or more blocks in between. The numbers on the top do the same as the ones on the left but only for the column. When all the fields that should be marked are so, you will end up with a picture that could be called pixel art. The order also matters. This means if you have a (5, 3, 4) you will have maybe some space then five adjacent fields to mark and then an unknown amount of space three more fields to mark the more unknown amount of space and lastly four fields to mark that may or may not be followed by more space.

Unfortunately, with the increasing size, the difficulty increases as well. So here are some tricks and why they work that will help you solve the harder ones.

### Look For The Full Size

 Edited Screenshot from  http://liouh.com/picross/

Quite a basic one, still one to mention though. If you find a row or column that mentions a number that is equal to the height or width of the Nonogram you can fill out the full row or column.

### Sum Equals Full Size

 Edited Screenshot from http://liouh.com/picross/
Similar to the previous one except now we're summing up all of the fields that need to be marked including spaces. In the screenshot we got 2 + 1 + 3 + 1 = 7. There are four groups of fields with each at least one space. Since ten is the maximum per line the spaces need to be exactly the size of one. So we have 2 + 1 + 1 + 1 + 3 + 1 + 1 = 10 with spaces being marked gray and fields blue. If the sum equals the maximum size of the picross (in this case the width, for columns the height) then we can mark them just as they're listed there since the spaces in between can't be bigger than one.

### Minimax Overlap

 Edited Screenshot from http://liouh.com/picross/
This is one of the tricks that I use most often. When you have a number that is big enough it creates an overlap that guarantees a field to be marked. Assuming we have a 10x10 picross with an eight. It could either lie from the top left to the right or it could be at the very right to the left. What we notice is that in both cases some fields will be marked either way. This leaves us with a guaranteed 6 fields. Fun fact: Regardless of the size of the picross if the number is greater than half of the height or width than this method starts to work for single numbers. It also works with groups as seen in the example below.
 Edited Screenshot from  http://liouh.com/picross/

### Default Overlap and Shifting

 Collage of screenshots made from http://liouh.com/picross/
For single numbers, the minimax overlap will swiftly turn into an automated thing. For example, if you have a 10x10 and you have a single number like six you know there are two fields in the middle that should be marked. Same for a 15x15 having 8 as a single number. You will start to instantly mark the middle field. Additionally, for every increment of that number, you can fill it by two more as seen in the example to the left.

Last but not least the shifting. The default overlap can be shifted easily. For this, we look at the numbers before or after. If the number is before it's a shift to the right if it's after a shift to the left. If it's on top it's a shift down if it's below it's a shift up. We need to count empty fields as well here. The example below shows it. The example is not the best though. If we have something like (1, 8, 2) it would work as we can assume at least one space between (1, 8) and (8, 2). No problem with that. However, if we have another number before or after such as (1, 1, 8, 1) it could be dangerous as we don't know how many spaces are between (1, 1).  So for (x, y, z), shifting works perfectly. For (..., x, y, z, ...) I haven't had enough experience and/or didn't look too deep into it.

 Edited Screenshot from http://liouh.com/picross/

### Try It Out :P

You can go and try it out under the gaming section of my blog (though I think I haven't updated those in quite some time... yikes.) or on other websites (there are tons). There are also free mobile apps. That's it from me for now. Happy brain work out!

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