Removing four lines at once with an I-piece in Tetris is the most efficient way to score, which creates a tension: on one hand, you want to build high enough to score quickly, but on the other, building too high puts you at risk of ending the game. The balance between the two is exquisite.
I mention that, because I was about to grumble that the corresponding balance in MEI Maths’s new game app thingummy Factris isn’t quite as good – of course it isn’t. Nothing ever will be.
This phenomenon is common enough to earn the name “the Tetris effect”.
Between getting hold of it for the ZX Spectrum in the 1990s and realising in 2007 that I had… let’s say a bit of a problem, Tetris was always my go-to game. At one point, I had the 17th-best score in the world on the Linux version and Tetris blocks falling in front of my eyes as I tried to get to sleep.
You can try to leave the glamorous world of world-class Tetris, but it always draws you back in for one last job.
Tetris and Factris
Tetris is mentioned, briefly, in my forthcoming book The Maths Behind…, available from October 2017, wherever good books are sold.
The game’s name is a combination of tetromino and tennis.
Here are the seven tetrominos of Tetris.
In case you lived under a rock for the entire 1990s, here’s how Tetris works: the game assigns you a tetromino, which you rotate and drop onto the pile of blocks below. Whenever you complete a 10-piece line across the board, the line vanishes and everything drops down; you get a bonus for removing several lines at once. When your blocks pile up too high, the game is over.
Factris takes the line-removal concept and gives it an arithmetic spin: instead of throwing down tetrominos, the game gives you rectangles of a particular area – anything from 4 to 16, but also the monsters 18, 20 and 24.
Instead of rotating the blocks, you can rearrange them into any pair of factors. A 6-block, for example, can be used as a horizontal 6 × 1, a flattish 3 × 2, a stubby 2 × 3 or a vertical 1 × 6. Primes, obviously, have only two possible configurations; 24, on the other hand, has eight possible ways to drop (In principle, at least – in practice, neither 1 × 24 nor 24 × 1 is possible). However, you’re only allowed to move through the possibilities in one direction – the pieces start as flat as possible, and become gradually taller as they’re resized (“Resized” is the game’s terminology. I reckon the size is constant, and we’re reshaping. Also, I will fight you).
You are shown the next five pieces you will be given, which allows a certain amount of forward planning; you are also allowed to discard a piece every twenty moves, which is often convenient when faced with monsters. You’re shown where the piece will land when it’s dropped, a development that would have probably made me even better at Tetris.
The game board is 16 squares wide and 16 squares tall, a design choice that has several interesting implications. Firstly, some of the pieces – the monsters – don’t fit on the board in two of their possible orientations. Secondly (a minor point), as long as you have space on the board, you can drop a 16-block horizontally and have it vanish immediately. (This is a useful way to buy time, or to get rid of a block without using up a discard.) Thirdly, and probably the key thing to Factris as a strategic game, is it opens up the possibility of clearing the entire board with a single block – removing 16 lines at once, a Factris.
And a Factris – like a tetris – means big points. Removing \(n\) lines at once scores you \( 50\cdot 2^n \) points, so a Factris is worth 3,276,800 points. Removing 12 lines at once is worth just 204,800.
But what is it for?
As far as I can make out, the idea behind Factris is to ingrain in its players the factorisations of the numbers in play. I can’t really speak to the effectiveness of that – I was pretty good with factorising small numbers even before I started – but I can easily believe that regular play would leave you with instant recall of the relevant facts.
You mean to say… that was maths? But I was enjoying it!
There are presumably side goals of improving speed of thought and general mathematical fluency – again, I can’t see how Factris could fail to improve those skills almost on the sly.
Is it playable?
I have some quibbles with Factris. I dislike the one-way nature of reshaping the blocks (for me, making and correcting mistakes is part of maths), but appreciate that this was a deliberate design choice – the makers consider that this would make the game too easy.
I’m also in two minds about the scoring system. In Tetris, you have a fair amount of leeway in scoring your tetrises because the board is five times as tall as the biggest block – once you’ve set up a column an I-piece will slot into, you can build elsewhere while waiting for it to arrive. By contrast, to get a Factris, you have to build to the top, you have to have a 16-block lined up next in the next two – and if not, you have to destroy your work. For me, the balance between skill and luck is a bit off here; I don’t instinctively feel that a 16-row clearance is worth 16 12-row clearances.
Original Mode allows you unlimited time, while Crunch Mode has a ten-minute timer.
Despite those grumbles, it’s a really addictive game. The strategy is rather deeper than in Tetris, and the pace a bit slower, giving the player a bit of thinking time. (That is balanced, at least in Crunch Mode, by having a certain amount of time pressure).
The Factris team is still adding tweaks; I look forward to seeing the improvements they still have up their sleeves!
You can reach the responsive development team at @MEIMaths on Twitter (or the hashtags #Factris #LikeTetris #ButMathsier).
Factris has a homepage on the MEI site.