Number Regions asks you to split the grid into regions and label each with its size. Every square gets a number; squares with the same number that touch along a side belong to the same region, and that region must be exactly that many squares.
So a 1 stands alone, a pair of 2s makes a domino, three 3s make a little L or a line, and so on. Two different regions of the same size can never touch along a side — otherwise they would be one region.
Start with regions that can only grow one way, and with gaps that are too small for anything but a small number.
Write a number in every square so that each region of joined, equal numbers has exactly that many squares.
The full guide, with a worked example and common mistakes: How to play Number Regions.
Yes — there can be many regions of 3, as long as no two of them touch along a side.
Yes — every puzzle here is checked to have exactly one solution.
It sets the largest region in the puzzle, which also keeps puzzles a sensible size to solve.
Open the Number Regions Solver, type the numbers and press Solve.