Akari is a puzzle made by nikoli.
In an unsolved puzzle, there are two types of cells, white cells and black cells. Some black cells are written with numbers.
To solve a puzzle, one must mark some white cells to be “lights”, represented by a circle in the example above. A white cell can only contain one light.
First, the number on a black cell indicates the number of lights which are orthogonally adjacent to the black cell. So a black cell with a zero has no light on immediate top, bottom, left, or right of it. At the opposite, a black cell with a four has lights in each of its immediate top, bottom, left, and right of it.
More, a light illuminates other cells. A light illuminates all the squares to each of the four directions until blocked with either the edge of the board or a black cell. So, in the solution above, R1C3 illuminates R1C2, R1C1, and R2C3. It doesn’t illuminate R4C3 since it’s blocked with a black cell on R3C3, and it doesn’t illuminate R2C4 either since the illumination path doesn’t travel diagonally. A light may not illuminate any other lights.
Some white cells must be marked as lights such that all white cells that don’t have any light on them are illuminated.
Walkthrough of the example
The example is actually very easy to solve. First, note that the 2 must have two lights adjacent to it. Obviously these must be R1C3 and R2C4; no other place for the light.
Now, look at R2C1. R1C1 is illuminated, so it can’t has a light. R3C1 is adjacent to the zero, so it can’t have a light either. So, to illuminate R2C1, a light must be placed on itself. The same goes for R3C2 and R4C3, so we completed the puzzle.