Fortunately, the game helps you a little bit here. Before you make a move, you can look at a little square at the top of the screen to see what kind of tile will appear with your next move.
The three kinds of number tiles are white, red, and blue. White tiles are multiples of three (though you don't know what you'll get), while a red tile is a 2 and a blue tile is 1. Red and blue tiles can only be combined with each other because one plus two equals three. So before you make your move, you'll see the color of the next tile at the top, and you can choose the move that will more likely bring you a matchable pair. If you had a 1 on the top of the board, for example, and you see a red tile at the top of the screen, you know that you're getting a 2, so you would swipe to situate that 2 close to the 1. Obviously it's difficult to explain, but once you start playing it will all become clear.
The other cool thing about Threes is how the game brings the numbered tiles to life. When two 3s are combined, you get a 6, but in Threes, a 6 is called a Thumbert (he even has a silly little bio), and the side of the tile has a unique smiley face that other combinations don't have. With the sound turned on, each of these "characters" has something to say when it first shows up. While that's kind of a minor detail, it gives the game extra life and keeps you motivated to keep combining.
The only thing that can get a bit annoying about the game is that the music gets a bit repetitive. Fortunately, you can turn it off in the settings, but that leaves only the silly voices associated with tiles, and without music the silly voices get a little creepy. It's certainly not a big deal, but probably worth mentioning.
Threes is an excellent game that only lasts a few minutes, making for a pick-up-and-play experience that's perfect for when you have just a little spare time. But while it initially seems like a sort of mindless swiping-and-matching mechanic, you'll need to use strategy to make sure you combine for big tiles to get the highest scores. This challenge is truly what makes the game addictive.
My only annoyance after playing the game for a while was that the music got repetitive. It's not a big deal because you can turn it off in the settings.
In short, Threes is an excellent time-waster that combines matching game mechanics with strategy and math to make for a fun diversion.