Ripple Effect (taken from Nikoli)
- The areas divided by bold lines are called "rooms". Fill in all empty cells with numbers under the following rules.
- Each room contains consecutive numbers starting from 1 (to $n$ where $n$ is the area of the room).
- If a number is duplicated in a row or a column, the space between the duplicated numbers must be equal to or larger than the value of the number.
Step by step
First fill in the two single-cell rooms with 1. Consider the left-hand one of these, and the two-cell room near it. If 1 is on the right of that two-cell room, then 1 can't be anywhere in the tetromino between. So we fill that two-cell room with
1 2. Then there's only one possible place for 2 in that tetromino between.
And the rest goes smoothly to the end. (Let me know if I should add more details here, but I've shown now how the deductions work, and once half the grid is filled the rest becomes relatively easy.)