This app was mentioned in 15 comments, with an average of 1.47 upvotes
Another Case Solved is a free offline puzzle game in which the solutions to the mini games make sense in the context of the crime for each case. It's very cleverly made and well-polished. https://play.google.com/store/apps/details?id=com.noodlecake.anothercasesolved
Another Case Solved - The puzzles you complete represent things a detective has to do to solve a case (finding clues, interviewing people, then using these clues to identify suspects and locations on the map, finally sneaking into houses to find evidence). The cases are tied together into a long story arch. It all makes sense and it's very rewarding if you're paying attention and not just killing time with some puzzles. https://play.google.com/store/apps/details?id=com.noodlecake.anothercasesolved
Retro City Rampage - It looks like many other pixel games, but it's actually an open world parody of GTA1 (before the series went 3D) with a lot of jokes about other games. It's funny, very polished and the game mechanics are very tight. It was originally a premium PSP title before it was posted to Android. https://play.google.com/store/apps/details?id=com.vblank.RCRDX
not rolling sky, you silly bot. this one: https://play.google.com/store/apps/details?id=com.noodlecake.anothercasesolved
Another case solved, the most respectable free app game I played. Best part is, they don't force you to use real money to get upgrades or clear a level.
The games I know that use this mechanic:
Another Case Solved, match clues to solve fun detective cases.
Puzzle Craft, match food and materials to build a village.
Deeply Absurd Chain, join items to find the next item in the chain and dig even deeper.