→ January 10, 2018
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Exit: The Game.

I have a new board game review up at Paste today as well, covering Pandemic: Rising Tide, a standalone spinoff of the best cooperative game on the market.

Exit: The Game won the Kennerspiel des Jahres in 2017 in a bit of an upset over the heavily favored and much better-reviewed Terraforming Mars, which I thought was the best complex game (or “expert game,” which is the literal translation of Kennerspiel) of its year. (It also beat Raiders of the North Sea, which I have played just once but enjoyed.) I’m guessing Exit won because it’s novel – it’s a series of cooperative puzzle games that are supposed to mimic the escape-room experience in a tabletop setting. There are other new games in this vein, like Unlock!, but Exit does this really well, with puzzles that you can reasonably solve in the allotted time and, more importantly, a very strong system for helping you if you’re stuck.

Each Exit box gives you a single play, because you’ll be changing destroying components, including tearing or cutting cards, marking up pages, and maybe even disassembling the box. I played four of the games: The Abandoned Cabin (the first in the series), The Forgotten Island, The Polar Station, and The Forbidden Castle, which vary from two to four on the game’s 1-5 difficulty scale, and there was a noticeable difference in the challenges – although I’m not sure the difficult boxes are better, just harder.

One Exit game box comes with three card decks – riddles, solutions, and help cards with hints – plus a booklet specific to that game, a disk of three concentric dials used to decipher codes, and sometimes some “special objects” that may be stencils or windows for finding clues on other cards or pages. You’ll start the game with one of the riddle cards plus the text on the first page of the booklet, and then must find a series of three-digit codes to progress through the game. Each game has roughly ten codes to find, represented by different shapes on the disk, which also help you figure out which cards and pages might work together. The puzzles come in lots of forms, and we found it was better to think a little like a kid to solve many of them. Some of the puzzles are visual – you have to trace things, connect dots, color in cards, fold pages into different shapes, cut pages into strips, all things you’d never expect to do with a board game. Some puzzles are self-contained, while others require you to solve three smaller ones to get each of the digits for the code.

Once you think you have the code for a specific puzzle, you locate that puzzle’s symbol on the outer rim of the disk and then rotate the three inner dials to match the code. (Some games use colors or other glyphs instead of numbers, but there will then be a reference card to help you translate them into numbers so it doesn’t become a drag on the game time.) A card number from 1 to 30 will show up in the center of the disk, which sends you to the Solutions deck. Some cards in that deck will tell you you’re wrong right away; others will ask where you saw that symbol – on a piece of furniture, a briefcase, a trunk, a door – in one of the images you’ve seen in the booklet or on a new card. You’ll then be directed to yet another Solution card, and if you were right, that new card will give you further instructions that will include at least one new Riddle card and perhaps give you a special object. This multi-step process makes it difficult to accidentally see an answer to a Riddle, and cheating via the Solutions deck would be nearly impossible.

Components from Exit The Abandoned Cabin
Components from Exit: The Abandoned Cabin.

The Hints deck is the cleverest aspect of Exit’s mechanics by far, and I think it’s what makes this game so playable even if you run into a puzzle you can’t solve. Every puzzle gets three Hint cards with its symbol on it, with the first card telling you what cards, pages, and/or objects you need to solve the puzzle (and maybe one small hint), the second card telling you most of the information on how to solve it, and the third giving the actual solution with an explanation. There were puzzles we solved without any Hints, and a few where we needed all three hint cards to move along. (The game has a timer app you can use, but there really isn’t any need for it except to let you know how long you’ve been playing and nudge you into looking at Hint card.) Having the first Hint card tell you which cards you must have to solve that puzzle is particularly useful if you have pieces of a few puzzles and aren’t sure which one to attack next.

Everything is fair game for solving these puzzles, including things like the game box itself, outside or inside, and each game we played had at least one puzzle that required us to use something that you might assume wasn’t part of the task. (The image on the inside of the top of the box in one game was quite faint, though, which I think is a mistake and makes the game less accessible.) We did find one glitch in The Forgotten Island, as the final riddle’s solution didn’t work; I haven’t heard back from the designer about this, but I’d pass on that particular module for now. The other three were all quite good and my daughter and I were able to solve them in about an hour using a few hints here and there; each had at least one eye-roller solution, but I think that’s the price of entry given that the designers have to come up with ten or eleven puzzles for each box, meaning some are going to be a little weird or ridiculous, especially when the designers, Markus & Inka Brand, try to make the riddles more difficult. The games list for $15-18 and, even as single-play games, they seemed like a good value to us, enough that we bought one after we finished the review copies I’d received (and my daughter will get some more for her birthday). If you’re intrigued, start with The Abandoned Cabin, since it’s first and I think the most straightforward of the four I’ve played.

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→ September 25, 2017
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For the love of algebra.

I have always loved math, and I don’t think there’s any field within math I love more than algebra. I certainly enjoyed calculus, and there are parts of number theory that still fascinate me (Goldbach’s conjecture, an unproven hypothesis that dates back to 1742, more than anything else), but algebra just speaks to me like nothing else in the domains of math or science. So when I saw this week’s FiveThirtyEight Riddler problem, which boils down to solving two equations for two unknowns, I might have dropped everything I was doing and spent about a half an hour solving it – messily, but I think ultimately getting the right answer.

My own personal love of algebra dates back to when I was ten years old, and my junior high school, lacking an honors math class for sixth grade, decided instead to bump me up to the regular eighth grade math course, where I met a wonderful teacher and some awful kids. (I was three years younger than they were, and of course small for my age anyway.) I was told very little about the move but somehow understood that I’d be learning algebra, so I went to the school library and found a book, long out of print now, called Realm of Algebra, by an author I’d never heard of at the time but would later grow to know very well through his science fiction writing, Isaac Asimov. I devoured the book, which I credit to Asimov’s ability to make even abstruse concepts clear to readers, in a weekend, and ended up ahead of where I needed to be for the class. Algebra felt to me like another language, as easy to comprehend as English, maybe even more so – like this was my native tongue and everyone had been hiding it from me. I could always “think” in numbers, but algebra gave me an entire framework for it, and everything I learned that year, especially from Asimov’s book, still directs much of how I think about problems today.

It has also made me an easy mark for puzzles and games that revolve around algebraic questions. I often check FiveThirtyEight’s Riddler questions, but I rarely try to solve them – some look too hard or involved, some just don’t grab me. This week’s question, about finding the area of a missing rectangle, hooked me from the start. (I suppose I should disclose that FiveThirtyEight is part of the ESPN network of sites, and thus I am connected to it as well.) Here’s the question in brief: Find the missing area in the picture below, bearing in mind that it is not to scale.

A puzzle of rectangles.

I tweeted the link to the article last night and got a slew of responses from readers, some right, some I don’t think were right, and a few that gave me more insight into the problem – one of which made me realize my first answer was impossible – so I decided to take a few minutes and explain my method, in case it’s useful to anyone or still contains a mistake.

To figure out the area of the lower-left rectangle, you need to know its height and width, so this is a problem of two unknowns, which means you need (at least) two equations containing those unknowns to be able to solve it. To make the math a little less messy, I defined the height (vertical axis) of the target area as 11-x and the width (horizontal axis) as 14-y, meaning that the height of the upper-left area is x and the width of the lower-right area is y. We know the area of the lower right rectangle is 45, and the area of the upper left rectangle is 32, so using the formula for the area of a rectangle we get the following two equations:

(14 – y)x = 14x – xy = 32
y(11 – x) = 11y – xy = 45

You can then solve one equation for one variable in terms of the other, substitute that back into the second equation, and solve for one of the two variables. I chose to solve the first equation for x, yielding:

x(14 – y) = 32
x = 32/(14 – y)

11y – y(32/(14 – y)) = 45

11y – 32y/(14 – y) = 45
11y(14 – y) – 32y = 45(14 – y)
154y – 11y2 – 32y = 630 – 45y
–11y2 + 167y – 630 = 0

That, my friends, is a quadratic equation, and if you remember your quadratic formula – where you take the two coefficients and the constant and plug them into the formula to get the two possible solutions – you can solve it from here, or you can just plug them into this site and get your two answers for y, which in this case are 7 or 90/11.

It turns out that both answers produce whole-number, positive results for the area of the lower left rectangle. If y is 7, x is 32/7, and the area is 45. If y is 90/11, x is 11/2 (5.5) and the area is 32. A reader pointed out that the first answer is impossible, however, because of the one number I haven’t mentioned yet: the truncated, upper-right rectangle’s area, which is 34. Because the area of the whole shebang has to be less than 154 (11 * 14), since there’s a piece missing at the extreme upper right, then the lower left area has to be less than (154 – 32 – 34 – 45), which is 43. That leaves 32 as the only possible answer. (EDIT: Fixed the second sentence, where I transposed the two answers.)

I think.

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→ October 31, 2011
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Lines of Gold app.

Boardgame designer Reiner Knizia has been active in pushing his games into the app space, with at least ten adaptations of existing physical games already available for iOS. He’s also moving into the puzzle-app space, with his latest release the $0.99 app Lines of Gold
icon, one I found strangely addictive even with a heavy element of randomness.

In Lines of Gold, the player has a board of 12 spaces connected in multiple lines of three that run horizontally and diagonally and must place tiles one at a time to try to create patterns where all three tiles match in at least one attribute across those lines. Tiles appear one at a time from the stack, so there’s little advance planning. Each tile has three attributes: color (copper, silver, gold); image (coin, bar/trapezoid, or wine glass); and number of images (1-4). A line with three of a kind earns points or extra tiles in the stack to extend the game; a line of three identical tiles earns a bonus round with entirely random results of more points or tiles.

However, any line of three tiles without any pattern costs the player two ways. There’s the loss of a tile from the stack, and there’s the loss of “pressure.” Every successful pattern moves up two gauges, one for scoring multipliers, another for “pressure” that in turn makes the scoring multipliers gauge move faster. A line without a pattern drops the pressure gauge back to zero – even if the same tile play produced a pattern on another line.

Once placed, a tile can’t be moved for any reason, and the limited number of spaces means you will often be forced to place a tile that will prevent you from creating a pattern on one or more lines. You get new spaces on the board once you fill the bottom two lines plus the left and right spaces on the line above that, at which point the board drops the bottom line and adds an empty line at the top.

At some point – I still haven’t figured out when exactly – a storage area opens up so that the player can store one (and eventually up to three) tiles from the stack, which makes the game play a good bit less random. In the first stage, you’re at the mercy of whatever tile comes up next, so other than understanding what tiles are more or less common (e.g., the copper tile with a single coin is the most common), there’s not a ton you can do to plan ahead. With two tiles available at any moment, you can sketch out a little more of a strategy – but at that point there are more tile types in play, so the game isn’t easier, just more of a thinking game than a quick-move puzzle game.

I certainly got my 99 cents’ worth by playing it four or five times over the weekend – a full game lasts 10-15 minutes once you get the hang of it, and I had one of about 20 minutes that put me (temporarily, I’m sure) on the global leaderboard – but overall I’d rate it behind the other Knizia puzzle app I’ve tried, ClusterMastericon, which is free to download but offers a 99-cent in-app upgrade to get more options within the game. ClusterMaster involves placing pieces of up to three colors on a hexagonal board of hexagonal spaces where you need to organize colored hexes adjacent to each other to make them disappear from the board. The “stress” game only lasts about 90 seconds, and there’s a lot more advance planning involved because of the limited number of shapes you might see and the balance between going for a large bonus (where you blow up a bunch of hexes at once through multiple patterns) and ensuring you don’t run out of room.

* My quick reaction to the Derek Lowe trade is posted now.

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