Goldfall Tower
You build one tower, and it's still there every time you come back. A block slides along the top, and a tap drops it where its shadow shows. When six blocks of the same material touch, they turn to gold and pour down into the lowest gaps. Only gold counts toward the tower's height.
The game plays offline and has no account. The shop sells optional Nugget packs, a one-time Starter Pack and Patron. If you agree, the app sends anonymous gameplay stats, which you can turn off in Settings at any time; see the privacy policy.