The Stack

I’m well on my way to clearing out the Special Crosswords. All I’ve got left is one that’s ornery and one that’s clueless. But to my surprise, there was one, which I solved last night, which was neither. Listed by an individual name, “War of the Words”, rather than by a type, it didn’t have a one-star difficulty rating like the Cluelesses or a three-star difficulty rating like the Orneries. It had two stars. What could it mean?

As you’ve probably already seen from the screenshot, it’s a crossword in the “barred” grid format, its words separated by heavier border lines instead of black squares. I remember seeing this format in the magazine. It’s basically a signal. It says “This one’s serious. It may even be British.”

Unlike everything else under Special Crosswords, it comes with no special instructions — just the normal explanation of how to scroll the clues and use the Hint button. This doesn’t mean there’s nothing special about it, it just means that you’re expected to figure out its special features without instruction. It doesn’t take long to discern that it’s a cryptic, just because the clues have that peculiar two-part cadence to them. But the designated cryptics have instructions about how to solve cryptics, and this doesn’t. I don’t think this is a mistake on the part of the game. I think it’s how it was originally published. And the thing is, a lot of the cryptic clues don’t quite work. Take 23-Across: “Sleep break”. The answer is “snap”. “Snap” is a synonym for “break”, and “sleep” clearly clues the “nap” part, but where does the inital S come from? Not from the clue. It goes against what I was saying about cryptics before, that the clues are self-contained and self-confirming. But in a puzzle like this, where you haven’t been promised anything about the rules, it just means that there’s a rule you haven’t discerned. Spot enough anomalies of this sort and you start to notice a pattern. And that’s a sort of puzzle I adore.

In this collection, there’s a bug that seems to be unique to this one puzzle, possibly because it’s in a different format than the rest of the crosswords: it tries not to select Down words. If you have a Down word selected, and you press enter to advance to the next clue, it will instead select an Across clue that crosses it. If you try to switch from Across to Down by clicking on the current square, it just doesn’t work. In most cases, I was able to find an uncrossed letter I could click on to force it into a Down, and once it was there, it obediently let me move the cursor around within that word. But there are some Down words that are crossed at every letter, and that makes them simply unselectable. Fortunately, the very conditions that make this happen mean that you can fill in every letter anyway.

Like the Cross Numbers, the Clueless is a form that arguably fits better in the Logic category than Special Crosswords. The basic idea is: You have an empty grid and a word list, and you have to fit all the words into the grid by deductive reasoning and/or trial-and-error. Unlike a conventional crossword, or even a Cross Numbers, the grid is highly asymmetrical, which is probably necessary to make the thing work.

As with the World’s Most Orneries, the Clueless puzzles are listed by unique names, rather than as “Clueless #1” or whatever. But it’s easy to tell whether a given thing in the list is Ornery or Clueless, because the Orneries all have a three-star difficulty rating, while the Cluelesses are all rated at one star. I really don’t agree with this rule. Some of the Clueless puzzles are vastly more difficult than others. One of the most useful tools in solving them is that the words come in different lengths, which cuts down on the number of places each word in the list can go. If, say, there are only two twelve-letter words in the list, that makes a very good starting point. But one of the puzzles uses only words of eight or nine letters, and another goes to the extreme and makes all the words the same length, just to take that crutch away from you. As of this writing, I still haven’t solved the latter. It’s the only one I haven’t solved.

Having at least attempted all of the Cluelesses, I have to say that I was a little premature in declaring that I had seen the game at its worst. I remember these things having problems, but I don’t remember them being as bad as they seem to be now. There are occasional typos, in both the words in the word list and in the solutions. That’s pretty much a given, considering the rest of the game. But typos in the word lists here are worse here than in other crosswords, because they can prevent you from entering the word into the grid. See, you don’t type the words in. You just click on a word in the list and a space on the grid. And it doesn’t take if the word doesn’t fit with the letters crossing it, even if it would fit if it were spelled right.

But the worse part is the Index Out of Bounds errors. When you enter a word, it gets greyed out in the list. Sometimes this makes something go wrong. The list stops displaying correctly, stops rendering at some point halfway down and throws an error whenever that point in the list is visible. This only happens with some of the words in some of the puzzles, and in most cases, it’s recoverable: just go to the next page and it’ll continue just past the point of the error. But that isn’t the case for the puzzle titled “Mars Attacks”.

In Mars Attacks, the word list is screwed up from the get-go. Click on a word, and it’ll enter a different word, one further down. Early in the list, the word you get is the one immediately below your selection. The gap between selection and result increases every once in a while as the list goes on. On top of that, entering pretty much any word makes it impossible to page to the portion of the list containing that word again without provoking errors that make it impossible to do anything other than quit the puzzle.

A rational person would just regard this puzzle as unplayable and move on, but then, a rational person would have given up on the whole game by now. After probing the puzzle enough to figure out the above, I realized that the only safe way to enter the words would be in the order they appear in the list, so that I never had to scroll the list backwards. To do this, I pretty much had to solve the puzzle on paper first. In the better-behaved Cluelesses, I found that using the point-and-click interface to try out ideas was a considerable aid to solving. But never mind, I couldn’t do that here. Once I had a full solution, I had to enter it without any mistakes, and even that took me a few tries. This took a measure of stubbornness well beyond what the game deserves.

But you know something? It’s not the most stubbornness I’ve ever needed in a game. Not by a very large margin. The puzzle isn’t supposed to be like this, but the experience is still recognizably ludic.

So, with the cryptics down, it’s time to turn to the rest of Special Crosswords. I discover I was mistaken earlier: there are several World’s Most Ornery Crosswords in here. My mistake stems from the fact that they’re not all listed together in the puzzle selection menu. Most puzzles are grouped by type, but that’s because the list is alphabetical and most puzzles have names like “Cross Numbers 1”, “Cross Numbers 2”, and so forth. But the World’s Most Orneries all have individual titles, like “A Manny Splendoured Thing” or “O. C. Can You Say”, alluding elliptically to the theme of the longer clues.

Apart from that, there seem to be only two other puzzle types I haven’t described yet. First, there’s the Helter Skelters. There are ten of them here. The idea behind them is that the clues aren’t separated into Across and Down because the words can go in any direction, including diagonals. Each word starts at a number and goes towards the next number, but there’s no indication of where the word ends. This is another of the puzzle types where computerization has a noticeable effect on the experience: on paper, you have to repeatedly pause to hunt for the next number, which is a distraction that can break the flow of clue-solving. These puzzles are on the small side, so it didn’t take long to get through them all. After doing half of them, I actually chose multiple puzzles from the main menu for once, to do the rest in a lump. The only real difficulty is that some of the squares, usually along the edge, have only one word passing through them. I know I’ve seen similar words-going-in-all-directions puzzles elsewhere that came with a promise of two clues per square, but not here.

Only one of the Helter Skelters here is severely messed up. In these puzzles, the cursor normally advances as you type, and does so correctly even on diagonals. But in this one puzzle, the cursor doesn’t advance at all — if you type an entire word, you’ll just repeatedly overwrite the same square. Even navigation with the arrow keys is broken. To enter a full word, I had to click each square with the mouse. And for my pains, I wound up with a score of 0% for that puzzle, because about half the letters in the game’s solution are blatantly wrong to the point of not even spelling pronounceable words. I assume this is somehow connected to the cursor movement problem, but I don’t see how. I suppose that it’s harder to spot major problems like this for a Helter Skelter than for a normal crossword because the actual solution looks like nonsense too until you trace through it. But I’d think someone would have noticed the problem if the game had received any playtesting whatsoever.

The other Special Crossword type is the Clueless, which I’ll describe in my next post.

I like cryptic crosswords. Not everyone does, but I do. I like the way they make me look at every word in the clues slantwise. I like how they show off the author’s cleverness, and make me feel clever for following their thought processes. And I like the way that the clues are self-contained and self-confirming. When you enter a word into the grid, you know it’s the right answer, because you built up that word out of pieces.

Or, well, sometimes you haven’t done that yet; particularly in these computerized ones, where erasure is free and doesn’t leave any marks, sometimes I’ll enter a word that I think is right without a firm idea of how it’s formed, just so I can figure out the rest of the clue by looking at it. But then, if I can’t figure out how it works, I’ll delete it. I’ve seen people who aren’t as hip to the cryptic ways as me fill in answers speculatively, without being able to explain the entire clue, and it bothers me. To do this is to treat it like an ordinary crossword, where you expect to get a few answers wrong at first because the clues are individually ambiguous. This is entirely the wrong mindset for a cryptic.

Anyway, I’m pretty sure that Games Magazine is where I first learned to do cryptics, so it’s good to see them represented here. There are eleven cryptics in Games Interactive, and I’ve found them to be the most pleasant thing in the entire collection. Not just because of the content, but because this is the one place where the UI really works. The puzzles are 15×15, so navigating with the arrow keys works properly, and they’re of the “lattice” type, with cross-clues on only half the squares of each word, which means that when you navigate out of the current word, you wind up in a square that has only one word going through it. Thus, it doesn’t keep switching me into an Across clue like the other crosswords.

However, true to form for this game, there are some bugs in the data. One puzzle has a misplaced number, with the result that you can’t fill in that word directly — and, unlike in the normal crosswords, the lattice format means you can’t work around the problem by filling in all the words crossing it. One of the official solutions puts an M where there should obviously be an N, creating the words “contemd” and “arsemal”. And one of the clues is “Load one admitted to prying”, which looks plausible as a clue in a cryptic, put which really should be “Loud one admitted to prying”. (The answer is “noisy”: “i” added to the middle of “nosy”.) I’m of two minds about the severity of this. On the one hand, I feel like cryptic clues need to be letter-perfect. On the other hand, I managed to figure it out anyway.

As promised, I spent much of the weekend on the two remaining Paint By Numbers sets, acutely aware as I did so that this is not the optimal use of my scant remaining hours upon this earth. But then, neither is whatever I would have been doing instead, so whatever. At this point, I’m pretty sure we’ve seen Games Interactive at its very worst and most grueling, and everything else will be relatively pleasant.

Let me talk a little about the process of solving Paint By Numbers puzzles. I usually get started by looking for rows and columns containing large numbers. In the extreme case, you have a run that fills its space entirely — say, you have a 25×25 puzzle and one of the rows is labeled “25”. That happened in one of the puzzles I just did, but it’s not common. More subtly, the numbers might leave only just enough space for a one-space gap between them, like if the same 25×25 puzzle has a row labeled “3 8 4 5 1”. The numbers add up to 21, plus four spaces between them. Most puzzles, however, don’t even have that, and have wiggle room even in their fullest rows. You can’t fill in the row entirely in that case, but you can often fill it in partially. Suppose you have a row “11 3”. If everything is in its leftmost possible position, the first number fills squares 1-11 and the second one 13-15. If everything is in its rightmost possible position, the second number fills 23-25 and the first 11-21. Since the first number fills square 11 in both its leftmost and rightmost positions, it fills it in all possible positions in between.

Once you have some stuff filled in, it starts acting as a constraint. The edges of the puzzle are particularly useful, because each square you fill in there nails down the position of a specific run immediately and absolutely. Any time you know the precise position of a run, it carves a space that must be unoccupied out of the perpendiculars at its boundaries, which can alter your analysis of what the leftmost and rightmost possible extents of things are. Often I wind up widening my area of certainty by one square, which allows me to be one square more certain in the other direction, and so on in a chain.

Now, this sort of logic can be frustratingly slow when you think you know what shape it’s making. It’s easy to say “Of course it’s symmetrical” or “It needs another leg” or whatever. But I prefer to stick to what I can reason out even then, because sometimes things aren’t quite the way you think they should be. They usually are, though, and people who let themselves fill in what they think is right probably wind up solving the puzzles a lot faster than me overall.

There is one situation where I tend to use my guesses about the picture, though: correcting mistakes. Sometimes I miscount something, or misread a number, or forget that I already have a square filled in at the opposite side of the puzzle, and I wind up with stuff that doesn’t fit together right. Unlike a lot of logic puzzles, I find I can usually recover from this without starting over completely. I just take one of the contradictory constraints and unravel it: Oh, so this is 10 squares long when the clue says 9? Let’s try erasing it on this end. That makes this other thing too short? Tack another square onto the other end. OK, but how did I decide which end to start with? Probably from my expectations of what the finished picture should look like.

After dithering with Cryptics for a while, I finally assailed Cross Numbers 1. It turned out that it contains only nine obviously nonsensical clues. I gave myself permission to use the Hint button without limit on those, but on my first pass with that rule, so great was my habitual reluctance to press that button it that I wound up only using it on one number. It turns out the clues contain a lot more information than is strictly necessary, so having nine clues that don’t really provide any information isn’t as big a handicap as you might imagine.

In particular, the ways that the clues reference each other means that you can often apply them in reverse. A clue like “34-Across: Sum of 9-Down and 12-Across” might as well be “9-Down: Difference between 34-Across and 12-Across” or “12-Down: Difference between 34-Across and 9-Down”. Really, the arrangement of the clues, the way that there’s a clue for each number in the grid, is a lie. You don’t necessarily figure out what’s in 34-Across from the clue labeled “34-Across”, and you’re not necessarily finished with that clue just because you’ve filled 34-Across into the grid.

Still, in my first pass I wound up with an irreconcilable logical contradiction. I restarted, this time taking hints for all the nonsense clues. I wound up with the same contradiction, but this time kept on going, ultimately getting a rating of 15%, even though the grid was mainly filled in correctly, just because of all the hint penalties I had incurred. Afterwards, I checked the game’s answers against the clues, and found that, as I suspected, my recurring contradiction was the result of a non-obvious mistake in the clues — one where the referenced numbers all exist and have a reasonable number of digits, but the math doesn’t work out as promised in the official solution.

This raises an interesting question: Given that there are multiple clues containing mistakes, how can I have any confidence in any of them? The answer is that correct things tend to confirm each other. If I have a number that already has a few digits filled in from the numbers crossing it, and I do some arithmetic to find that number and get an answer that fits the digits in place, that tends to convince me that the clues for both that number and the numbers crossing it are valid. Even better: If I notice a contradiction, and check my math, and find a mistake that resolves the contradiction, that really gives me trust in those clues, because it shows that I can trust them more than I can trust my own thoughts. Because of this, I had a pretty good idea of which of the seemingly contradictory clues would turn out to be wrong: it would be the one with the least confirmation. This turned out to be the case.

It strikes me that one could make a puzzle out of this, similar to how diagramless crosswords were, according to legend, originally inspired by an incident where a crossword’s clues were accidentally delivered for publication without a grid. The challenge would be to find the deliberate mistakes in the clues, given that most clues are error-free. To make it easier, you could let the solver know the exact number of mistakes — although if you did that, you could reject solutions that don’t have enough mistakes!

Anyway, I’ve tried to figure out what the faulty clues were supposed to be, to see just how badly things went wrong here. It turns out that most of them are pretty close to something reasonable. The most common error, apart from leaving off the second term of a sum, is just mixing up Across and Down.
Here’s my list:

• 15-Across: Sum of 3-Across and 34-Down: Should be 30-Across and 34-Across.
• 17-Across: Multiple of 45-Down: Should be 45-Across
• 21-Across: Sum of 46-Across: …and 32-Down
• 46-Across: Average of 35-Across and 57-Across: 57-Across should be 57-Down
• 61-Across: Sum of 47-Across: …and 50-Across
• 69-Across: Sum of 16-Across: …and 9-Down
• 9-Down: Square of 71-Down: Should be 71-Across
• 24-Down: Product of 24-Across, 47-Across, and 68-Down: 24 Across should be 25-Across
• 40-Down: Product of 48-Across and 70-Across: Should be 58-Across and 70-Down.
• Finally, the stealth mistake. 16-Across: Sum of 46-Across, 61-Across, and 42-Down: The best I’ve come up with for this is replacing 46-Across with 25-Across. But that’s a relatively unlikely typo, so I’m not really satisfied with this solution. Maybe there’s a better one that has typos in two of the terms.

I remember attempting the Cross Numbers puzzles in Games Magazine, but I’m not sure I ever actually solved one. I always found them intimidating. They’re dense tangles of interreferential logic, with clues like “Product of 33-Across and 30-Down” and “Number of 5s in the completed grid”. Such a thing offers no obvious foundation for solving; everything depends on something else, and finding so much as a toehold is difficult. Sometimes you have to notice that you have a couple of digits in a six-digit number that’s clued as the square or cube of some other number and there’s only one square or cube of that length that has those digits in those places. The instructions advise using a calculator. I prefer a spreadsheet.

There are two Cross Numbers in the Special Crosswords section of Games Interactive. (I’d have probably have put them under the Logic section, because they’re the sort of puzzle solved through deductive reasoning, but I can understand why they’re classified as they are.) They are positively the biggest mess I’ve seen in the whole game so far.

My first inkling that there was something wrong was a clue “Multiple of 45-Down” where there is no 45-Down, just a 45-Across. This turned out to be just one of several clues referring to things that go in the wrong direction. Perhaps it just had the directions swapped in these cases? But no, the clue for 24-Down is “Product of 24-Across, 47-Across, and 68-Down”. There is no 24-Across, and it can’t really be talking about 24-Down because then 24-Down would be itself multiplied by a couple of other multi-digit numbers. Another of the clues is “Product of 48-Across and 70-Across”. Not only is there no 70-Across, but 48-Across has six digits while its alleged multiple has only four.

Did they just include the wrong grid or something? Maybe, but that doesn’t explain the even weirder clues, like “Sum of 46-Across”. Sum of 46-Across and what? Maybe it meant to add together the digits of 46-Across? But no, in one place it asks for a three-digit “sum” of a single two-digit number. I suppose that could be explained by the grid being wrong too. But I’m still reluctant to accept this because the other Cross Numbers puzzle uses the phrasing “digit sum” for such things.

When I looked at the second puzzle, it was mainly to see if the two puzzles simply had each other’s clues. It turned out that the second puzzle doesn’t have the problems of the first, and is actually in solvable condition. It does have some problems, though. There’s a square erroneously colored black: you can move the cursor into it and presumably type a number, but you can’t see what you typed. 62-Down is shown in the wrong place, in the middle of 56-Down, with amusing consequences for navigation. The clue for 88-Down is missing, resulting in an “Index Out of Bounds” error dialog if you select it in the grid. Fortunately, the game recovers gracefully from this.

I did solve the second puzzle — a possible first for me, as I’ve said. The game rates my solution at 88%, but I trust my reasoning more than its judgment. I haven’t entirely given up on the first puzzle either: it’s possible that its nonsense can be overcome through copious use of the Hint button.

Games Interactive seems to have only one World’s Most Ornery Crossword. I suppose that’s fitting. The magazine only ever carried one per issue, as a sort of capstone to the “Pencilwise” section. If they had published more than one at a time, it would cast doubt on the “World’s Most” claim. Things are no different here.

There are two distinguishing things about World’s Most Orneries. First, there’s the size. The grid is 25×25, which is larger even than the Sunday puzzle in the New York Times. The makers of Games Interactive decided not to fit this all onto the screen at once, instead making it scroll vertically, even though they really didn’t need to. Even under the constraints of the game — running at 640×480 resolution, with a 43-pixel header and a 50-pixel footer — there’s room enough for 25 rows of 15-pixel squares, which is large enough to hold the font used for the clues, along with a black line separating rows and a two-pixel margin. As it is, we instead have 19-pixel squares. 25 rows of 19 pixels takes 475 pixels. So perhaps 19 pixels was chosen because it’s the largest size that they could use and still fit an entire World’s Most Ornery Crossword on a 640×480 screen. If so, it’s too bad they messed it up by using up vertical space with headers and footers.

Selecting a word, whether with keyboard or mouse, automatically scrolls the grid to make the entirety of that word visible. This is fortunate, because the scrollbar is unreliable. Navigating between words with the arrow keys is also broken: trying to move up or down instead moves the cursor a bunch of spaces left or right. I haven’t probed this deeply, but I’m guessing that the navigation code is assuming a 15×15 grid, the size of all the easy crosswords in the collection.

The other distinguishing feature of the WMOC is that it has two sets of clues: the Hard Clues and the Easy Clues. In the magazine, the Easy clues were printed on half of an adjacent page, with the intent that you’d use the Hard clues by default and could switch to Easy by folding the page over. Resorting to Easy always felt a little like cheating, but it was at least a relatively honorable form of cheating. In Games Interactive, there’s a button for switching to Easy, but, interestingly, it only affects the currently-selected word, minimizing the cheat factor.

There’s another cheat mechanism shared by all the crosswords in the game: the Hint button, one of the few ways that the puzzles in this game benefit from being computerized. Pressing this button deducts a point from your score and reveals a random letter in the current selected word, possibly a letter you’ve already filled in correctly. I’ve resorted to requesting hints on a few occasions when the puzzles expected me to know the names of athletes or musicians, but it’s not clear to me if it hurts your score less than just getting a letter wrong. Anyway, even though Easy is cheaty, and the game treats it as such, it doesn’t consider it to be the same sort of cheaty as Hints. Easy doesn’t affect your score at all. The only motivation you have for not dropping down to Easy is your own sense of honor — which is the case for a lot of computer games, come to think of it.

I guess it’s time to move on to the Crosswords section. Actually, I’ve done a fair number of them already. I wanted to get a jump on them simply because it’s by far the most numerous section, and also I find they make a good palate cleanser between other puzzles. They’re so reassuringly easy! Games Magazine gives its puzzles a difficulty rating from 1 to 3 stars, and the puzzle selection menu in Games Interactive displays these ratings. All the puzzles in the Crosswords section, without exception, are rated at 1 star.

“But not all of the crosswords in Games are easy!” you may be saying. “Some of them are even World’s Most Ornery!” Those are off in the Special Crosswords section, along with the Cryptics. We’ll get to that. Keeping the easy crosswords separate from the hard ones is a good idea if you think your players are going to let the game select them at random, because a one-star ordinary crossword and a Cryptic are certainly not adequate substitutes for each other. But then, as I’ve said, I don’t think the randomization feature in this game is at all useful.

The crossword UI here is less annoying than I remember. When I first played it, it was weirdly slow to respond to input. I had seen web-based crosswords written in Javascript that were more responsive, and I didn’t really understand what it could be doing that was more wasteful of resources than running in circa-2000 Javascript. After a general system upgrade failed to make it noticeably better, I concluded that it must actually have some kind of deliberate built-in delays. But it runs so much better on a machine built approximately 15 years later that I guess it really was just wasteful code after all.

The UI is actually mostly pretty reasonable. At any moment, there is a cursor at one square in the grid, and an entire word space highlighted, along with its clue. You can navigate arbitrarily by clicking on either the clues or the grid, but I don’t like doing that. Because interacting with a crossword consists mainly of typing in words, I want to keep both my hands on the keyboard most of the time. And it lets me do that. Pressing enter moves to the next clue, cycling from the last Across to the first Down and vice versa. In the easy puzzles, I can fill in most of the grid on a single pass through the full clue list, so navigating this way is optimal. The harder ones are another matter. There, I want to go straight from filling in a word to considering the clues that cross it. You can move the cursor around arbitrarily with the arrow keys, but there’s one problem: when you do that, it automatically switches you to an Across clue. You can switch to Down by clicking the current square with the mouse, but as far as I can tell, there’s no way to do it from the keyboard. I haven’t looked at other computer crossword interfaces in a long time, but I’m guessing that by now there’s a semi-standardized hotkey for that, known to all enthusiasts.

There’s also a bit of a problem with erasure, because it uses the Backspace key for that. Backspace normally deletes the letter before the cursor, but if it applied that rule consistently, you wouldn’t be able to delete the last letter in a word. So it applies it inconsistently instead. I think what I’d really like to do is use the space bar to erase the current square and advance the cursor as normal. That is, I want it to act like a text editor in overwrite mode. As it is, the space bar moves the cursor forward without changing anything — which is the same thing that all unrecognized keys do.

Paint By Numbers must have been good training for Battleships, either in solving technique, or in attaining the right mindset, or simply in finding patience. Whatever the reason, I’ve managed to power my way through the rest of them.

Not that I got them all right. Oh, I had a good run of solutions that were recognized as perfect, but then suddenly it judged a couple in the last set as massively wrong. I’m not sure what to think about this. I said before that some puzzles were ambiguous, but I’m no longer convinced this is really true — it could just be that I failed to spot my own mistakes. Certainly my lengthy run of correctness suggests a lack of ambiguity in the puzzles, and in the ones I got correct, I often spotted and corrected inconsistencies just before submitting. On the other hand, there are enough outright mistakes in the game as a whole that it’s very easy to lose faith in its correctness. One of the trivia questions references a picture that isn’t included, at least one of the crosswords has a word that extends into a black square, at least one of the word puzzles under Special Crosswords contains typos in its word list that make it literally impossible to solve completely, and so on. Things that you’d expect QA to catch. But I suppose I’d trust the game about the Battleships more if I had a better idea of what it thought was wrong in my solutions. When you submit a Battleships solution, the game displays corrections highlighted in pink, but the corrections cover up what the grid was like before the corrections were applied.

Battleships done, I finished going through the rest of the Logic section (apart from Paint By Numbers). The only repeated puzzle type I haven’t mentioned yet is “Cross Math”, which is sort of like a generalization of magic squares. You put the digits from 1 to 9 into a grid, but instead of each row and column having the same sum, each row and column must satisfy a unique equation. I find that these puzzles are best approached mainly through trial and error, aided by a certain amount of deductive reasoning to limit the number of possibilities, like “The first operation in this row is division, so either the first number is composite or the second number is 1”.

Then there are some one-offs, most of which aren’t really logic puzzles. Like, there’s one about matching dance step diagrams to their names, which seems like it belongs in the Trivia section to me. I was so dissatisfied with my score on this one that I retried it until I did it perfectly, and discovered that even perfection was rated as only 20% (or 50% with the time bonus). Presumably the wrong maximum score was entered for that puzzle. Just another of those little mistakes that make me lose faith in the thing.

Another of the puzzles belonged better under the Visual category. It shows a picture of a complex arrangement of gears, and asks which direction you have to turn a handle at one end of the whole chain to make the gear at the other end turn clockwise. The arrangement is three-dimensional, with gears at different angles, and the picture is so low-resolution that I was never quite sure what was going on in the joints where a shaft met another shaft at an angle. Nonetheless, I managed to get the right answer, if only because even a completely random guess comes out right half the time when there are only two possibilities.

There’s only one one-off puzzle in the Logic section that I’d call a proper logic puzzle, and it’s one of those ones where you have to figure out attributes of a group of objects on the basis of clues. Specifically, this one was themed around a television schedule, and had clues like “The shows that air at 8:00 on Tuesday through Friday have first letters that are alphabetically consecutive” and “The three shows with colors in their names all air on the same day”. This is a type of puzzle that’s only made less convenient by computerization. Solving it takes pencil and paper. The in-game grid of time slots doesn’t help particularly.

On my first attempt at this puzzle, I really thought I had run into ambiguity again. I had a partial solution that seemed to satisfy all of the clues, so any way of filling in the rest of the shows had to be valid. So I entered a solution, received a low score, and concluded that there must be a clue missing. Only the next morning did I think that I might have gotten a clue wrong, by thinking in terms of what’s showing at 10:00 when the clue was actually about what starts at 10:00. (Some of the shows are two hours long, so airing at 10:00 and starting at 10:00 are not the same thing.) And sure enough, paying attention to the exact wording revealed exactly that, and with that additional information I was able to solve the puzzle. So the mistake was mine, but on the other hand, it was way too easy to believe that the game had left out crucial information.