Pair Sum shows a grid of numbers and a target. Tap two that add up to it to clear them, and new numbers drop in. Quick clears build a multiplier, the target moves, the grid grows to 5x5, and triples (three numbers) appear later. A wrong pair costs 3 seconds, and every board has a valid answer.
Yes, every board and every new target has a solution.
Some targets need three numbers, which are worth double points.
Yes, the daily uses a fixed seed.