The Stack

It is with some relief that I report that I have finished the Paint by Numbers puzzles, and made some progress on the Battleships. I’ll be closing out the Logic section entirely before long, and that will leave just the three most lightweight categories: Trivia, Visual, and one that’s new to Games Interactive 2: Word Search. I haven’t mentioned the word searches yet, because they’ve never been the focus of my play sessions. And yet I’ve almost finished them.

Let me get this out of the way: Word searches are a joke. They’re the puzzle type that fans of all other types of puzzles look down on. Logic puzzles require real thought, crosswords test your knowledge and vocabulary, and cryptograms combine all of the above, but all a word search requires is the ability to not be bored by word searches. The reason I’ve gotten so many of them done is that I’ve been doing them one at a time between other puzzles in order to avoid having to do them all at once. It’s one thing for a variety puzzle game to have one or two word searches for variety’s sake — one per issue of the magazine was pretty much the right amount, if you ask me — but this game has twenty. That’s more than any other single puzzle type except crosswords.

The word searches from Games Magazine have one real point of interest: The unused letters spell out sentences, usually some quotation linked to the puzzle’s theme. As far as I know, this was never stated outright in the magazine. It was just a little bonus for those who noticed it. The closest they came to spilling the beans was in a March issue with an Irish-themed word search for St. Patrick’s Day: the editor’s message for the issue mentioned that the editor had suggested slipping some Irish names into the unused letters, only to be told “Wait til you see what we’ve already got going on there”. So at that point, not even the editor of the magazine was in on the secret. But that anecdote was enough for me to catch on, and now, the information proves useful: looking for the hidden sentences provides a welcome shortcut to finding all the words, in addition to making the whole process less tiresome.

As you’re probably expecting if you’ve been following these posts, there are problems. There are occasional typos in the word lists: SUBSITUTE for SUBSTITUTE, BARBEQUE where the grid contains BARBECUE. Such words cannot be marked in the grid; the game only accepts what’s in the word list. Occasionally there’s a word that’s left out of the word list entirely. You can tell that it’s supposed to be part of the solution because it interferes with the secret unused-letters text, but it’s just not there. One particular puzzle is missing something like half of its word list. I only have a vague sense of what the unused letters were supposed to spell out in that one. In one of the puzzles, part of the grid was actually misplaced, showing letters one space to the right of where they should have been. It took me a while to figure out what was going on there. Once again, I find myself thinking that some of these bugs could make good puzzles in their own right if deployed deliberately.

The UI is mainly reasonable, but has one biggish problem: words are marked with ovals around them, and these ovals are sometimes wide enough to intersect with adjacent letters, especially when the ovals are diagonal. Now, the puzzles come in different sizes, and the larger grids are fit on the screen by using a smaller font. Throw a couple of lines across the smaller font and it becomes illegible. It’s not hard to think of solutions to this. Like, instead of circling the words, put a line through the marked letters! Ideally, make the line a light color and display the letters on top of it so you can still read them. But I suppose you can’t do that in the print version, so it violates the game’s prime directive.

Unexpectedly, I seem to have found a new technique for use in Paint by Numbers: eliminating possible positions for a run along an edge (either the natural edge of the grid, or any line past which you’ve eliminated any possibility of occupied squares) by considering how the perpendiculars affect the next tiers inward. For example, suppose the leftmost column in the grid says just “7”, and the column adjacent to it says “5”. It follows that the run of 7 must either have no rows in common with the 5, in which case it coincides with seven rows that start with 1, or have enough rows that begin with something other than 1 to accommodate the 5. That is, if you have seven rows that start with 1 except for one in the middle that starts with 2, that can’t be where the 7 goes, because it would place an isolated square into the second column where it can’t be part of the 5.

It’s obvious when you think about it. (If it doesn’t seem obvious from my description, my description is to blame. It would probably be clearer from an illustration.) But it’s a thing that’s easy to not think about, especially if you’re plugging away at the more usual techniques. The only thing that made me start thinking about it in this way was a sequence of puzzles that pretty much relied on this sort of reasoning, having lots of one-thick outlines around the edges.

I understand that popular logic puzzles, like nonograms and sudoku, have names for specific techniques. I don’t know the names, though, because I haven’t studied the theory. To me, finding the techniques yourself is part of the fun. Which I suppose marks me as a programmer.

While I’ve been stuck on the Battleships, I’ve been progressing through the Word Puzzles. I finished them today. I haven’t been posting about them because I don’t have much to say about them. It’s exactly the same assortment as in the first Games Interactive: Bulls Eye, Mind Flexers, Quote Boxes, and Solitaire Hangman. But I do have some complaints, which I’ll make now.

One of the Bulls Eye puzzles calls for a word that can be formed from the first letters of a sequence of words in the instructions, but the instructions are apparently not the same ones this puzzle was originally printed with, so that clue is impossible.

One of the Hangman sets is composed of highly unusual words, like “ouabain” and “buprestid”, which is basically cheating. I remember playing Hangman as a child: the other children would say “Oh no, it’s Carl! He has a large vocabulary, and will doubtless choose an obscure word none of us know!” But I recognized even then that this would be a cheap victory. The true triumph is in choosing a word that’s perfectly common, but that they still wouldn’t guess, like “shoebox”. And that’s what most of the Solitaire Hangman sets are like, apart from this one. I can’t say that it was completely impossible, though, because I managed to get the word “siphuncle” right, despite not knowing it, just from guessing likely letters. The twelve most frequent letters in the English language are ETAOINSHRDLU, and applying those to “siphuncle” yields SI_HUN_LE with only five wrong guesses. And of the remaining letters of the alphabet, the ones most likely to appear before an H are C and P — which just happen to be the letters we need in the word.

And finally, there’s a certain amount of repetition. Two of the Quote Boxes sets use the same Elizabeth Taylor quote about people with no vices. Even worse, Hangman set 6 is simply a repeat of set 5 in a different order. I can believe that they’re just copying stuff from the magazine, and that the magazine repeated puzzles occasionally. But it’s definitely something that should have been caught before publication.

Once again, I seem to have gotten stuck in a pattern of starting Battleships sets and not finishing them. It’s funny: when I finished the last of the Battleships in the first Games Interactive, my reaction was one of relief that I would never have to do this again, even though I knew there was an entire additional volume of the things waiting on the Stack. The Paint by Numbers sets may take a great deal longer than the Battleships, but I’m finding the Battleships far more onerous. I think this is because Paint By Numbers is marked by near-continual progress. It can get slow, but you’re always improving your knowledge of what’s in the grid. Whereas in Battleships, I can just plain get stuck. It makes me think there’s got to be some approach I haven’t discovered yet, some way of looking at the grid that simplifies the impenetrable.

I do think I’m doing better than I did in the first game. If nothing else, I’m managing to check for mistakes before submitting my solutions pretty consistently. (The UI changes help here.) But the fact that I’m aiming for real solutions in the first place is pure stubbornness on my part, given how contemptible a production it is, and especially given that I’ve already cheated. Finishing this game obviously means solving the Final Puzzle, and, lest we forget, you don’t actually have to solve any other puzzles to do that. You just have to attempt them. Actually getting them right is effectively a side quest.

But if I were the sort of person who’s willing to just skip over the content to get to the end, I probably wouldn’t be writing this blog. Look: It bothers me that I cheated my way past the final boss in the South Park FPS. I recently got a bunch of Sonic the Hedgehog games in a Humble Bundle, and I’ve been contemplating putting Sonic CD back onto the Stack. That’s is a game I played before starting this blog — at the time, it was the only Sonic game for PC. I played through every level and reached an ending, but it wasn’t the good ending, and I’m thinking lately that it shouldn’t count. I have similar twinges about my suboptimal completion of Police Quest 3. So I have good reason to believe that if I don’t do my best to complete Games Interactive 2 for real, it’s just going to haunt me later.

I find that there are two distinct modes of thought involved in solving Battleships puzzles. It’s not quite the “logic vs intuition” thing again, though.

On the one hand, you have the same sort of approach as Paint by Numbers puzzles: proving things about the grid. You have certain constraints, including puzzle-specific ones like “this row has exactly three occupied spaces in it” and general ones like “there is exactly one set of four consecutive occupied spaces”, and from these constraints you construct chains of reasoning about what must be in specific spaces. “There are two three-tile long ships and only three places where they can fit. So at least one of them must be in one of these two places, both of which border on this square. Therefore, this square is unoccupied.” You then mark the square as unoccupied, and start using that as a constraint in further proofs.

On the other hand, you can also think of it as an assembly puzzle, like pentominos or tangrams. You have ten pieces of varying length, and you have to put them together into a shape that fits certain constraints. True, most assembly puzzles use a target shape where the pieces touch each other, and that’s specifically forbidden here, but that doesn’t really make much difference. You’re still thinking about it in terms of moving pieces around. There’s typically a very limited set of places where the four-long ship can go, so you try it out in one of those places, and when you see that it prevents the rest of the pieces from fitting in nicely, you move it somewhere else. This is really equivalent to reasoning from trial-and-error, but I find that conceptualizing it as moving pieces around makes it a lot easier. Sometimes I’ll mark in all the pieces in an way that doesn’t fit the numbers, because it helps me to see how to fix the problem by moving something.

Usually my trajectory through a puzzle starts with the former approach, and switches to the latter when progress fizzles out. In some puzzles this happens very quickly. Notably, the UI discourages the assembly model. I can think about it in terms of moving pieces around, but I can’t actually remove an entire ship from one place and put it somewhere else as an action. The only form of interaction is marking and erasing individual tiles, which fits better with the other approach. This sways how I want to solve the puzzle. I can’t blame Games Interactive for this, though. The same applies even more strongly to the print version.

As before, Paint by Numbers is weekend work. The game has six sets. I’ve done two so far, and expect to manage a third today, leaving the other half for next week. The palette this time is missing the dithered grey that I previously used to mark uncertain squares, so I’ve been using yellow for that purpose instead. At least the two-semantically-distinct-whites problem is gone.

The chief characteristic of Paint by Numbers is that it’s methodical. I described the basic solving process in a previous post: you look for a thing that just barely fits in the space available, which gives you information about its position, which imposes constraints on other things, and so on. It takes time, but you can keep on extending the chain of logic for as long as you keep finding leads. Every once in a while, though, the chain seems to end. Maybe you reach a point where the necessary reasoning takes more steps before yielding concrete results. Maybe there really is a simple next step, but it’s hard to spot. Either way, I wind up marking, in a different color, the things that I suspect rather than just the things that I know.

I don’t like taking this step, because it seems so much less certain than the plodding and methodical reasoning. But is it really? In theory, logic should never steer you wrong, but it’s being applied by a fallible human mind. I frequently do make mistakes. Occasionally, I even make mistakes so severe that I have to correct them by wiping the entire grid and starting over. Intuition may well be a better guide, especially as I train it up by solving these things. It would certainly be faster. I remember struggling with anagrams in crosswords as a child, seeing no good way to solve them other than by writing down every possible arrangement of letters to the point where they stopped making sense. Nowadays, all I usually have to do is look at the letters and, if I have enough constraint from the cross-letters and clue, the solution just pops out at me unbidden. Could a human mind get to the point of solving nonograms the same way? I suspect so, given the prodigious mental feats that “Human Calculators” have trained themselves to do. Heck, after all this intensive practice, I may well be closer to that point than I’ve been allowing myself to acknowledge.

I decided to ease myself back into the Logic section by tackling the one-off puzzles. This time around, it turns out none of them are logic puzzles in the traditional sense. There’s an easy tile-based dissection puzzle, a memory challenge, a sort of visual trivia thing where it gives you the top and bottom thirds of a bunch of circular logos and other symbols and you have to match them up. This last one has a non-intuitive UI: all the pieces are displayed on the screen at once, but whenever you want to match a pair, you have to click “Done”. I don’t think I’d have guessed that if I hadn’t seen it do something similar in the Cryptograms.

There’s one puzzle in the assortment that I could see calling a logic puzzle, although it’s really more of a math puzzle. It’s a more complicated variant on the old chestnut where you’re given a head count and a leg count and have to derive how many cows and how many chickens there are. The premise here is that there’s a planet occupied by six species of aliens with lame jokes for names. The number of eyes, noses, mouths, eyebrows, ears, and heads varies by species. Given a total count of each body part, can you figure out how many of each alien there are? Well, maybe you could in the magazine. Here in Games Interactive 2 it’s impossible because they left out the body part count. That’s like asking us to solve a crossword without the clues. We’ve seen other puzzles where there was information missing, and I’ve always done the best I could. But this time, the best I can do is just hit the “Done” button and let it give me a rating of -100% for not having any of the answers right.

Well, I’ve completed the Special Crosswords. The remaining Orneries fell in a single session. It’s a lot quicker to get these things done when you’re fully alert, and can get your mind into a thinking-of-words zone. But then, it’s also quicker to get them done when you already did half the puzzle in a previous session, and that’s probably the larger factor here.

That left just the sole remaining Clueless, which was one of the difficult ones I mentioned before, where all the words come in just two lengths and there isn’t much obvious constraint about what goes where. Such a puzzle offers no clean way to get started. The only workable approach I’ve found is trial-and-error, picking a space with lots of crossings and trying out each of the words from the word list in that spot and exploring the consequences until you hit an impossibility. If you’ve picked a good spot — which I didn’t on my first couple of attempts — then you eventually find a word that forces a lot of other words, and the pattern grows until not being right would be a weird coincidence. If you haven’t, you eventually find a few different words that don’t force anything much.

This last and hardest Clueless turned out to be the only one in Games Interactive 2 with a typo in the word list: the word “power” was listed twice and “loser” omitted, as if the extra power had forced the loser out. Fortunately, due to changes in the UI, I was able to get a perfect score anyway. In the first Games Interactive, if you tried to put a word in a place where it conflicted with existing letters, the game just didn’t let you. In Games Interactive 2, it lets you and it just overwrites any conflicting letters. And the way the word “loser” was situated, it had words crossing it at the L and S. So I could put “power” into its spot, then re-enter the crossing words to overwrite the P and W. I can’t help but think that there’s a metaphor in that, but I don’t know what.

I said that I hadn’t done the World’s Most Orneries. I have, however, been attempting them. I think I’ve tried them all by now, mainly because I wanted to confirm that they were World’s Most Orneries — as before, they’re listed only by title, not type. But I’ve only finished two. This is because I keep drowsing off.

Really, you can blame my current schedule more than the puzzles (or the music, which I haven’t even been listening to). A World’s Most Ornery takes takes me about 1-2 hours to get through, which is certainly something I can manage in most circumstance. It’s about the same amount of time that I’d spend on a Battleships set, for one thing. But I haven’t even been trying the Battleships lately, because they require more focus. If start to nod off in the middle of a logic puzzle like Battleships, then drag myself awake and remember “Right, I was in the middle of a puzzle, I should finish that”, I’m basically lost. Puzzles of that sort involve storing information in your head about what implies what. Crosswords don’t. I can go straight from drifting off to looking at a clue with exactly the same level of bafflement that I started with.

I think I’d stay awake better if the game better afforded breaking the monotony by alt-tabbing out to a browser window, if only to start preparing a blog post. It doesn’t prevent you from doing this, but it keeps the screen resolution at 640×480, which is so unsuited to modern use that it hardly seems worth it.

Failing to make much headway on the Logic puzzles, I’ve skipped ahead to the next section, Special Crosswords. It’s a similar assortment to last time. The Cross Numbers are gone, but we’ve got World’s Most Ornery, Cryptic, Helter Skelter, and Clueless. They’re all quite revamped and less buggy than before. This comes as a particular relief for the Clueless, which was previously nigh-unplayable, and now functions perfectly, albeit more slowly — you used to be able to scroll the word list by an entire page at a time, but now it dribbles out line by line. And I’m pretty sure there are fewer typos than before, especially in comparison to the regular crosswords. It’s enough of an improvement that I’ve guzzled down the lot, apart from the Orneries, which take a while, and the hardest of the Cluelesses, which features only 9-letter and 5-letter words.

The changes to the UI have an effect on the Helter Skelters that’s worth noting. One of the distinguishing things about the Helter Skelter is that you can’t tell just from the grid where the words end. The first Games Interactive recognized this by not limiting your typing, even to the point of letting you type past an edge and wrap around to the other side. In Games Interactive 2, Helter Skelters bide by the new rules for all crosswords: when you select a word, the space for that word is highlighted, and you cannot move the cursor outside that space. This is effectively a change to the rules. It gives you information that you don’t have in the print version. Sure, some of the other puzzle types make information more easily accessible than it would be in print, like the letter frequencies in a cryptogram, but that’s still just information you could gather for yourself.

The one thing that makes it a bit more like the print version is that the word length indicated by the highlight is sometimes wrong. Not often, but often enough to make me never trust it as a source of information.