An origami house that can rearrange itself in eight different ways? It won’t surprise you to learn that this concept home is based in part on the work of a famous mathematician and puzzler.

Fun, puzzly iPad apps are popping up at such a rapid pace these days that it’s getting hard to keep up. Why, I might spend hours in a day, sitting on my sofa solving puzzles and playing games. I hope I have your full appreciation for my sacrifice. Let’s catch up with some recent offerings, spanning a wide range of categories:

Abstract Logic: Huebrix

My current chief addiction, of the “gotta solve just one more” variety. At its most basic level, each puzzle requires you to fill the screen with an assortment of colored bricks. (Or, I suppose, “brix”). The bricks start off in little piles — there are fifteen red ones in the pile above — and all you have to do is trace a finger along a path, and watch the bricks fall into place. Get a brick in every white square, and victory is yours.

Simple enough, in theory. But then the curveballs start coming. The paths you draw must adhere to an increasingly complicated assortment of rules: Your path can’t turn in certain spots but has to keep going straight. Or, your path has to end at a particular point. Or, certain squares must contain a brick of a given color. Wait — I keep saying “or.” Actually, it’s just as likely that a puzzle will require you follow all of these rules simultaneously — all of these rules and then some. The hardest puzzles will truly make your brain sweat. Even some of the advanced “easy” puzzles gave me pause.

The basic game is .99 and comes with over a hundred levels — and you can buy other puzzle sets, each for an additional .99. I’ll be buying several, I’m sure.

Physics Puzzles: Freeze!

You’re an eyeball. (Look, don’t ask questions.) You’re an eyeball, and you’re trapped in a macabre series of mazes — mazes where the walls have jagged teeth, or lasers block your path, or scythes swing merrily through the air. You need to reach the swirly exit point so you can get out of this nasty place… and, well, into the next nasty place.

You have two things going for you: You can rotate the maze, causing yourself and anything else affected by gravity to tumble merrily around. And on certain levels you can hit the Freeze! button, which allows you to suspend your eyebally self in midair — a neat trick that will often allow you to avoid certain death.

Some games hold your hand for a while before pushing you out to more advanced levels. This is not one of those games. The mazes here get tricky mighty fast, and I would not blame you if you thought, now and again, that a particular puzzle is impossible. Stick with it, though — with perseverance, a steady hand, and an excellent sense of timing, you can make it through every maze. (Or at least every maze in World 1, of the four worlds available. Heaven knows what awaits me in World 2…)

Word Games: Letterpress

For a while there, my friends were getting excited about one word game after another, and every one of those games was really Scrabble in disguise. Lexulous? Scrabble. Words With Friends? Scrabble. Come on, already. Aren’t there any other multiplayer word games that contain a healthy dose of strategy?

Yes: Now we have Letterpress. The rules could not be simpler: You and your opponent work from the same set of 25 letters. (These letters stay the same for an entire game.) Make a word, and capture the letters that you’ve used. When all the letters have been used at least once, the game is over — the winner is the player who has claimed the most letters. That’s it.

The easy rules — and stripped down interface — belie a ferocious game of staking out and defending territory. Letters that are surrounded by a player’s color cannot be stolen away, and so both players try their best to secure the most frequently used letters. Long words are all well and good, but more often the winning strategy is coming up with words that nibble away at your opponent’s bank of letters. Of course, your opponent is trying to do the same thing to you. Once a word is played, it cannot be played again, so the longer the game continues, the fewer options you’re likely to have. Between two evenly matched players, Letterpress is often won by a mere point or two. It’s a worthy alternative for Scrabble lovers.

For Kids: Crayon Physics

An independent hit when it first came out for the PC, Crayon Physics has been delightfully ported over to the iPad. To get the little red circle over to the star, just draw whatever tools you need — boxes, levers, platforms, wheels. This is a wonderful first physics puzzler for children, and perfectly good fun for grownups, too. And the basic version right now is free in iTunes, so what could you possibly be waiting for?