Recs.
Updated
Brain It On! is a free-to-play puzzle game where physics are essential to solving the puzzles. The player is presented with a couple of different physics problems, and it's up to you and your drawings to complete the level.
Specs
Pros
Pro Hours of fun finding different solutions
This remains my favorite phone game of all time. After getting all stars on all the levels, I can just restart and do it all over again and not end up doing things the same way the next time though on many of the levels. It is a game that makes you think and can grab and hold your attention like very few mobile games can. Everyone should give this one a try.
Pro Fair monetization system
The game is free to download and while there are in-app purchases, they are certainly not required to progress naturally in the game. Levels are unlocked in groups of five, and if you manage to complete four of these five levels, the next set of levels is unlocked. If you're stuck, you can watch a video advertisement in order to receive a hint. Most players won't have to spend money at all to fully complete Brain It On!, but you can pay around $3 to unlock all levels immediately.