Jum Noli – Release Announcement & Solving Guide
Jun 29th, 2009 by AlexWeldon

In the games section of the site, I’ve just posted six examples of a puzzle I invented, called Jum Noli. It’s inspired by Japanese-style number puzzles like Kakuro and Sudoku, but in keeping with my tastes, I’ve tried to make it “denser.” The small grid and tight restrictions mean that most Jum Noli puzzles require just one or two leaps of logic to get the first few boxes filled in, after which the solution usually comes quite quickly. Making that breakthrough, however, can be quite challenging.


As explained in the puzzle PDF, the objective is to fill in a 4×4 grid of boxes, placing one, two or three dots in each box.

There are two restrictions in placing the dots. The first is indicated by the numbers next to the rows and columns; these indicate the total number of dots that there must be in that row or column. The second is indicate by the dots inside the diamonds. These indicate that the surrounding four boxes must have a clear majority of that number of dots – thus, two or more of the boxes must contain that number of dots, and no more than one may contain any other particular number. That is, if the diamond shows three dots, the surrounding boxes could contain [3, 3, 3, 1] or [3, 3, 2, 1] but not [3, 3, 2, 2].

Each puzzle has only one solution. Finding it typically involves applying logic to determine with certainty how many dots must go in specific boxes, then using that information to make similar conclusions about other nearby boxes, and so on. Usually, once 6-10 boxes are filled, the rest will be much easier, but how does one go about filling in those first few boxes? It’s easiest to explain by means of an example. Let’s start with the grid to the left.

One trick to apply is to look for the highest and/or lowest row and column numbers in the grid, because there are fewer possibilities for how to arrive at those totals. As an extreme example, if a row showed a 4, you would know immediately that all the boxes in that row contained a single dot. Likewise, if it showed a 12, all the boxes would contain three dots.

This puzzle doesn’t have any 4s or 12s, but it does have an 11, which can only be made with three sets of three dots and one set of two. The obvious question to ask, then, is which box contains the two dots. Looking at the two diamonds at the top of that column, we can see that the group of two dots must be in one of the top two boxes – if both of those boxes contained three dots, it would be impossible to obey the requirements imposed by those diamonds.

The left diagram shows one possibility. The right diagram shows the other, but we can eliminate this as an option. If the top box of the second column contains 3 dots, then the only way to make the top row add up to six is for the remaining boxes all to contain a single dot. However, the top right diamond requires that it be surrounded by a two-dot majority, which creates a contradiction. Thus, we can firmly place two dots in the top box of the second row, and fill the rest of the row with three dots in each box.


The next step is easy. The top left diamond requires that the surrounding four boxes contain a clear majority of one-dot groups. Since two boxes have now been filled in with a two-dot and a three-dot group, the remaining two boxes must clearly contain a single dot.

After this, however, the puzzle gets a little trickier.


Looking at the third column, we see that it must contain a total of six dots. There are only two ways this can be accomplished; either with one group of three dots and three singles, or else two groups of two and two singles. However, the key thing to notice is that none of the middle three diamonds contains a single dot. This means that nowhere in this column can there be two consecutive single dots! This rules out the first possibility, and also combinations like [1,1,2,2]. The only possibilities are [1,2,1,2] and [2,1,2,1].

All we can do is try out these two combinations and look for a contradiction. It turns out that it’s easy to find one. If we try [2,1,2,1], we find that the top right corner must also contain a 1, in order to satisfy the top row total (6). This conflicts with the top right diamond, which states that it must be surrounded by a clear majority of two-dot groups.

Eliminating this possibility, we arrive at the following result, at which point the rest of the puzzle should be very easy to solve, since most of the rows and columns are almost complete. I’ll leave it to you to finish it:

Hopefully this example helps illustrate the sort of techniques needed to solve the puzzles. Of course, they vary widely in difficulty; some will only require reasoning at the level of the first two steps of the example – others will require even greater leaps of logic than in the third step. I’ve even managed to come up with puzzles that I myself can’t solve (though I’ve written a simple computer program to verify the existence of a unique solution).

Typography Tutorial – Matters of Space pt. 1
Jun 12th, 2009 by AlexWeldon

It’s about time I got back to talking about typography. Up until now we’ve been discussing how to choose the appropriate typeface(s) to set your text. Many people seem to think that this is the big issue in typography, but it’s really only the tip of the iceberg. Actually putting the characters on the page is not as trivial as it might seem.

The usefulness of a wide right margin

The usefulness of a wide right margin

Type is a fluid. It’s compressible, but only to a certain extent. It can be shrunk or expanded to fit the space available, but there’s only a small window of comfortable pressure – expand or condense it too much, and the readability starts to suffer. What you can do, however, is adjust the shape of the container; type, at least in English, has the nice property of being composed mostly of short words, so the lines can be broken up into all sorts of different lengths, so the same passage of text can be rearranged into any number of shapes and aspect ratios, as long as the total area on the page remains roughly the same.

Most non-designers, when putting a document together in word, simply use a single column, with the default margins. If they need to include pictures, they’ll often put them in at the top or bottom of the page, or if they do put them in the middle, will often interrupt the text above the picture and resume it below. This is equivalent to using a bucket for all one’s water-containing needs. Sure, it’s very practical at times, but it’s hardly the thing to impress dinner guests. Sometimes, it pays to be more creative with text placement.

The horizontal width of a block of text is called its “measure.” Unless the text is justified, the length of an individual line will typically be less than the measure; the measure is the maximum length of any line within the block. Justification is the process of forcing every line (except, usually, the last line of a paragraph) to be exactly equal in length to the measure, thus having clean edges at both sides, as opposed to a ragged margin.

There are a number of reasons one wants to have control over the measure, and like most things in typography, there are always trade-offs to be made. Making the measure wider can help fix awkward spacing in justified text, and is usually slightly more efficient in fitting text into a small area on the page if the paragraphs are long, as every line break represents a little loss of space, since the words usually won’t fit exactly into the space available on the line. However, expanding the measure also brings associated problems – the longer the line, the harder it is for the eye to trace its way back to the beginning of the next line, decreasing readability by increasing the number of times the reader will lose his or her place. Also, if the text contains many short paragraphs, wider measures can actually be less efficient, as a great deal of space is lost when a paragraph ends partway through a line.

Using a sketch to plan layout

Using a sketch to plan layout

There are two ways to change the measure. One is to break the text into columns. On a portrait-oriented 8.5×11 page, two columns are often optimal, as 7.5-8 inches is actually an extremely wide measure, usually too wide – the proliferation of single-column typed documents is mostly a throwback to the days of typewriters, but even in this day and age of powerful word-processing software, the majority of people haven’t outgrown this Dark Age in typographical history, due to a combination of habit and lack of understanding of the technology.

The other thing you can do is to adjust the white space on the page. Changing the width of the left and, particularly, the right margin of a page will result in a corresponding change in the measure. If you have more than one column, you can also adjust the gutters, that is If your document contains many images and/or is likely to be read by someone who might want to take their own notes, having a wide right margin is a very good idea! It allows pictures to stick halfway into the text and protrude out into the margin in an aesthetically pleasing fashion, and provides a convenient place to take notes.

Remember, too, that you needn’t stick to one measure for the whole page. Balance and harmony are important, but especially for text with natural divisions, and when there are images that can be used as visual dividers, you can split the text up into different areas of the page and vary the margins and columns between them. You can also use typeface variations as discussed before, to further create a separation between the different sections.

The key to creating a nice design in these cases is to experiment quickly by means of sketches, before starting to set the actual text. Using lines for text and crossed-out boxes to represent images, do some brainstorming – come up with as many viable layouts as you can before settling on the one that provides the best organization of the information and the most aesthetically pleasing page.

Addictive pacing in games
Jun 3rd, 2009 by AlexWeldon

A recent thread on IndieGamer brought up the subject of addiction in games. The original poster linked to several articles on the subject, which discussed both how to create addictive gameplay by using constant small rewards, and also the ethical issues that have been raised, now that the very most addictive games, such as MMORPGs have begun to have increasingly documented detrimental effects – including death – in their heaviest users.

For some reason all these articles focus on the idea of achievements and item collecting, but neglect what I consider to be an equally-important aspect to making a game addictive: granularity/stopping points.

When stepping away from something, we naturally want to stop at a convenient lull in the experience. If I’m working on a piece of art, I’ll usually stop after finishing some object or area of the canvas. If I’m reading a book, it’ll preferably be at the end of a chapter, but if the chapters are too long, I’ll instinctively try to find a place where the end of a paragraph and the end of a page coincide, so I can start at the top of the next page when I come back to it. If I need to pause a rented movie for whatever reason, I’ll wait until right after a particularly important scene.

I think most, if not all, people play video games the same way. The easiest games to put down are ones divided into levels (or larger levels, divided into smaller waypoints), which take maybe 10 or 20 minutes to play. The decision whether or not to continue playing is thus broken into finite, significant, but manageable chunks. If there’s something else we need to do, eventually we will decide that we don’t want to commit to another 10-20 minutes, and it’s easy to put it down because we feel we’ve reached the end of a chapter in the story, and the game is giving us permission to stop there and come back later.

If you want people to stay glued to your game, rather than playing in such increments, there are two things you can do. One is to make the “chapters” longer, but this is a questionable strategy, as people will be less likely to come back to your game at all if they know they’re committing to an hour or more before they reach a good stopping point.

A much better, and more common strategy, is to make the gameplay either continuous, or make the bites so small that it’s always possible to play “just one more round.” This can be likened to the potato chip/candy phenomenon – no matter how full, guilty or nauseated the eater is feeling, they always find themselves reaching for just one more chip or gummi bear, since the commitment each time is so small. You can observe that the phenomenon decreases with something slightly larger, like a cookie, and disappears almost entirely with something on the scale of a cupcake.

Many Flash games take this model. I played a beta version (no public release yet) of an addictive little shooter called Bullet Time the other day; instead of featuring levels and a win condition, the game was merely about surviving as long as possible. Of course, it offered degrees of achievement for surviving 15 seconds, 20 seconds, 30 seconds, 40 seconds, and so on… With games rarely lasting more than a minute, the temptation to give it one more try is very hard to resist, no matter how many “one more tries” you’ve already given it.

You can combine the two versions of the strategy, of course. The Civilization series is a good example. Games of Civilization (or its sequels) generally take so long that few gamers will play all the way through in a single session – thus, the primary stopping point is rarely reached. However, the game is broken into a series of turns, which usually do not take very long to play. Thus, the player is constantly tempted to play “one more turn” before saving and quitting. This is compounded later in the game by the fact that with so many cities and units present, there is almost always one that is on the verge of something exciting – one turn away from capturing an enemy city, one turn away from finishing a World Wonder, one turn away from a scientific discovery, one turn away from finishing the last unit needed to fill a transport ship and send it off to war…

I’m not an MMORPG player myself, but from what I’ve heard, they also employ a mixed strategy in this way; the everyday grinding of monsters is a continuous experience, with the time commitment to seek out and kill one more foe being very small, and thus difficult to escape from. Meanwhile, raids are apparently a very large time commitment, and impossible to put down partway through – especially since there are other real human beings counting on you.

In a way, this form of addictive gameplay is more insidious than the achievement/reward system, though of course the two effects are hardly mutually exclusive. The latter, at least, gives the players something they enjoy – what’s good for the developer is also good for the players, at least in moderation. However, decisions about stopping points are a bit trickier, ethically. As a player, I appreciate games that give me a convenient way of sitting down for what I know will be a finite and predictable amount of time. As a developer, on the other hand, I would love nothing more than to suck a player in, and have them spend much more time playing my game than they had intended. Even disregarding the problems associated with real addiction, there’s something a little bit shady about giving people something that’s less good for them as a consumer because there’s an advantage to you as the provider.

Of course, in talking about games, players usually use “addictive” as a positive descriptor. At least on the surface, it appears that game addiction is a consensual relationship. The armchair psychologist in me wonders if this is really the case though, or whether it’s actually a perfect example of post hoc rationalization: “I sat down to play this game for 15 minutes and ended up spending two hours instead. Therefore, the game must be really fun.” Is fun something that is determined by the player’s emotional state while engaged in the game, or by their tendency to play for long periods of time and/or come back for more? The two don’t necessarily go together, especially when coupled with a personality type that is prone to procrastination and feelings of guilt for doing so.

Those especially interested in the whole issue of game addiction may be interested to know that there is a 122-page thesis on the subject. I don’t know if I’ll have time to read the whole thing, but I’m definitely tempted to try.

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