Web Paint-by-Number
How to Create Puzzles

This site provides tools to allow you to create your own paint-by-number puzzles. Most people make puzzles for other users of this site to try to solve. Some people just make puzzles to print out and use as a gift for another paint-by-number fan.

It's pretty easy, but not quite as easy as just drawing a nice picture. Not all pictures make good puzzles. In fact, most don't. Some are simply impossible to solve. Some have more than one possible solution, so that the person solving it will have to guess which solution is the one you intended.

There is no way to be sure a picture is workable as a puzzle, except to try to solve it yourself, or to use a computer program to try to solve it. This web site allows you to test puzzles either way before you "publish" them to allow other users to solve them. It is not unusual to have to do many iterations of editing and testing before you get a puzzle that looks good and solves nicely.

But there are things you can keep in mind while you draw your picture that will make it more likely that the puzzle will work well. By following these guidelines you can often come up with an image that will work fine on the first try. On the other hand, none of these guidelines are hard and fast rules. Some of the very best puzzles are the ones that break them.

## Guidelines for Solvable Puzzles

The little two-by-two puzzle below is the simplest example of a puzzle with two possible solutions:
 A Tiny Puzzle One Solution Alas, Another Solution

One of the key things to watch out for when making a puzzle is to avoiding having this little two-by-two pattern appear anywhere in your image. That can be a bit tricky, because if you make line drawings, then it is quite likely to come up whenever you have a diagonal line.

Take, for example, the smiling face below. You'll find instances of the little two-by-two diagonal in four places around the edges of the face. Any or all of these could be flipped to get another solution to the puzzle, as shown in the second picture. In fact, when there are a few of these in an image, it usually means that all sorts of disasterous alternate solutions exist, some bearing little resemblance to the intended solution, such as the potato salad in the third picture.

 A Happy Face An Alternate Solution And Another

How do we fix such problems? Well, as a general rule, you do it by filling in more cells. Less white generally means less trouble with multiple solutions. There are many approaches that can be used. By keeping some of these ideas in mind while drawing the image in the first place, you can often get good puzzles on the first try.

One of the most common fixes is just to "thicken" the diagonal lines. Here's a version of of our happy face with thicker lines. We've added more black cells turning the diagonal lines into stair-steps of black cells instead of just pairs of cells touching only at the corners. This version of the puzzle has a unique solution, though it's actually fairly hard for a tiny puzzle. Examples of puzzles that use thick lines include #45 and #168.

Notice that in the mouth we still have pairs of cells that touch at the corners. That's OK though, because they touch other cells at the faces. You don't always have to eliminate all corner touches. You can often get away with leaving a few in here and there. But the general rule is to make diagonal lines thick, not thin.

A less common way to make thin diagonal lines work is to "crowd" them. For instance, in the puzzle below we have filled in the corners. The two-by-two diagonal lines are still there, but they are so close to other cells that if you tried flipping them, they would merge into the corners, and violate the clue. This version of the puzzle is quite easy to solve. Another example of crowding a one pixel wide line to make it solvable is in puzzle #413.

A variation on this idea is to use a different color to "pot" or "embed" the picture, as shown below. We just fill some of the surrounding space in with an alternate color. The result often looks pretty good, but it tends to result in an excessively easy puzzle, so it isn't really that great a method. Puzzle #355 is an example of a line-drawing potted for solvability. Puzzle #133 uses the same trick in a more limited way.

Generally speaking, puzzles with more colors are easier. So you can often make an unsolvable puzzle work by judiciously "colorizing" it. Here we've colored bits of our original puzzle to give one that has only one solution. Puzzle #413 is another example of a puzzle that was unsolvable until it was colorized.

Our smiley face does a pretty good job of filling in the image grid. There are no big blank white spaces anywhere. If you do larger line drawings, this is often not the case. In fact, simple line drawings on a large grid almost never prove solvable unless there are at least a few rows and columns that are mostly filled in. One way this can happen is if you choose an images with strong vertical and/or horizontal lines in them that span much of the image. When drawing an image, you might consider making near vertical lines a bit more vertical and near horizontal lines a bit more horizontal. Puzzle #394 is an example of a line drawing that is solvable only because it has many strong verticals and horizontals.

Sometimes if a puzzle proves unsolvable, filling in some of the white area with other objects or added detail can help. Puzzle #390 originally had a lot of white space, which was filled with four extraneous objects to make the puzzle solvable.

Really though, you are more likely to end up with solvable puzzles if you don't think in terms of line drawings. Instead of just drawing an outline, fill in the image. Large areas of solid color make a puzzle much more solvable. A silhouette of a horse is much more likely to work than an outline of a horse. The solid smiling face below is easier to solve than most of the outline drawings above.

So, some guidelines for making puzzles that are likely to be solvable are:

1. Avoid thin diagonal lines. Use thick lines instead.
2. Use large areas of solid color.
3. Use strong verticals and strong horizontals.
4. Use lots of different colors.
5. Don't leave large areas of white space.

If you follow all these rules, you are almost certain to get a solvable puzzle, but it is almost certain to be a very boring, very easy puzzle. Puzzles that break a few of these rules, are likely to be much more interesting and challenging. Personally I'm always impressed when a puzzle designer can break the rules and still come up with an attractive, solvable puzzle.

## Drawing the Picture

Of course, a good puzzle is not only solvable, but also has an attractive image to reward the solver when they are done. And, really, that's where you start when making a puzzle: just drawing a picture.

Obviously it helps if you can draw. I'm not really much of an artist myself. I can impress small children with my ability to draw cats, pigs and race cars, but I can't draw, say, a recognizable portrait of a specific person. If you can really draw, I'm sure it will help immensely, but people of modest artistic talent can make good puzzle images too.

First, this is probably the most forgiving of all artistic media. You can fiddle with your image for as long as it takes to get it looking right, and never leave behind any smudges and smears to reveal that the final image is really just the result of a lot of trial and error. If you can recognize a good image when you see one, and if you are patient, then there is no reason you can't eventually get a puzzle image worthy of Michelangelo.

Second, remember that even Michelangelo can't draw a great picture of a horse on a 20-by-20 pixel grid. If your image is recognizable, you are already leading the pack. Nobody expects to see the horse's nostrils flaring and his mane blowing in the wind. The artistic standards aren't terribly high here. Though if you can manage to hint at a blowing mane, we'll all be mightily impressed.

Finally, practice helps. Just as you quickly get better at solving these puzzles, you quickly get better at making them.

I almost never attempt to draw anything out of my head. I always try to have a picture to work from. Sometimes I produce an almost exact rendering of the original image, sometimes the puzzle ends up only roughly similar. But it helps me a lot to have a model to work from.

Where do I get model pictures? Google Image Search. This is a great way to quickly find images of almost anything I can think of. And when I can't think of anything, I type in random words and see what comes up. (Which probably helps explain the sheer randomness of some of my puzzles.) If you click on the "Advanced Image Search" link, there is an option for searching only for black & white images. This can be nice when looking for inspiration for two color puzzles.

When choosing an image, you want to avoid those with important details that are too small compared to the total image size. I once tried to do a version of the Girl Scout Logo, which is kind of a clover shape with three profiles in it. I found that for the profiles to be recognizable as profiles, the lips and noses and curves of the foreheads had to be very accurately rendered, which meant they'd need to be quite big. But since these details are small compared to the size of the logo, the total puzzle size would have had to be very big to come out looking good. In the end, I gave up on that puzzle.

Finally, there are a few categories of puzzles that tend not to make very interesting puzzles. These include:

Text Puzzles
These puzzles just contain words, usually in block print. They are usually neither very interesting to solve nor very interesting to look at when you are done. That doesn't mean you shouldn't ever use words in a puzzle. Words combined with pictures can be cool. An unusual font design can also help.

Flags
If you solve many puzzles on this site, you will eventually hit a puzzle showing a flag of somebody else's country. You will naturally be inspired to produce a puzzle showing a flag of your country. The problem with this is that the vast majority of the world's flags have very simple designs and, if presented unimaginatively, make very boring puzzles. The flags which do make half-way decent puzzles are already well represented on the site.

So if you want to do a flag, try to present it in some imaginative way. At the very least, draw it waving in the wind. Or show it flying over the heads of the heros of the great revolution as they defend the barriers with pitchforks. Or use it as a background for a portrait of the much beloved under-secretary of educational reform.

Symmetry
Symmetry tends to make puzzles less interesting to solve. So you should generally do things to break up symmetry, either choosing a non-symmetrical image to start with, or just arranging the pixels a bit differently on the two sides. There is no reason that the wings of a butterfly have to be pixel-by-pixel identical. Puzzle #1333 is a nice example of a symmetrical image varied just enough to make it unsymmetrical to solve.

When I've got an image I like, I start up the puzzle editor in another browser window, picking an image size that seems right (though I almost always end up resizing the canvas before I'm done) and then moving browser windows around on my screen so I can see the canvas and model image at the same time.

Here's a some helpful hints on image editing:

• You don't have to click on each individual cell. You can move the mouse while holding the button down to paint a bunch of cells at a stroke.
• The arrows below the grid shift the image up or down, or to the left or right. Very handy.
• The white and black paint buckets below the grid will erase or fill in connected regions of cells, as in a standard paint program.
• You can resize the puzzle grid. Just save the puzzle, and afterwards you'll be given the option to edit it again with a new size. If you plan to reduce the grid size, you'll want to shift the image to the top left and figure out the new grid size you'll want before saving. It'll be cropped off at the bottom and the right.

So I draw the picture. Fiddle, fiddle, fiddle with it until it looks OK. When I'm getting it close to what I want, I hit the "Check" button at the bottom of the screen.

The check button runs a fairly powerful computer program that checks to see if the puzzle has more than one solution. If it reports that there are multiple solutions, it will let you see one of them. You can toggle back and forth between the alternate solution and the intended solution, and get an idea where things are going wrong. If the whole image is going wrong, you'll probably need to make big changes, if it is just in one little area, just adding a few pixels in that vicinity might do it for you.

Sometimes the checker will report that the puzzle is logically solvable. It does this if it was able to solve the whole puzzle using only techniques that normal humans use. If it says that, then you've definately got a workable puzzle, though I still recommend doing a manual check to see how it solves.

If it says the the solution is unique, but it doesn't know if it is logically solvably, the you should test it yourself. It is entirely possible to create a puzzle that the computer says has a unique solution, but which is next to impossible for any mere mortal to solve. You really need to check it yourself.

To do this, give the puzzle a temporary title, then save it, without checking the "publish" box. On the next screen, you'll be able to click "try solving".

First thing I do when I'm playing my new puzzle is click the "helper" button. The "helper" is a much stupider puzzle solving program than the "checker". It will never mark a square that a careful human couldn't find, and will actually miss quite a few that a clever human would find. It takes a moment to run. If it finishes with the puzzle solved, then I know I've got a solvable puzzle. If it fails to solve the whole puzzle, then that may not necessarily be a bad sign. The helper is dogged but not really very smart. It will fail to solve many perfectly good puzzles, especially ones with colors. (In fact, it can only solve a few of the smiling face puzzles on this page.) But if you look over the unsolved part of the puzzle yourself, and fill in a few more pixels here and there that it missed, you can click the helper button again and it may be able to finish the rest of the puzzle.

Note that the relative dumbness of the helper compared to the checker is a deliberate feature. The point is to determine is if a human can reasonably solve the puzzle, so a solver that is stupider than a human, but which is willing to accept help from you, is a much better tool for assessing the solvability of a puzzle.

If it appears that the puzzle is unsolvable, I take note of which parts of the puzzle image weren't solving. I then return to the editor, and try fiddling with those parts more, mostly filling in more cells. I keep going back and forth between the editor, the checker, and test solving until I get something the helper can solve (with or without my help).

When I think I'm done, I clear the board and solve it completely manually as a final test. Only then do I return to the editor to enter a final title and description save it with the "publish" button checked so other people can try it out.

If you are trying to make an especially difficult puzzle, then you can keep going beyond this point. You can do things like looking for what pixels you can delete without making the puzzle unsolvable, or you can blot out some clue numbers, if you like that sort of thing.