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'Picross' or 'Nonogram' is a puzzle game similiar to Sudoku and other Japanese Puzzle games.
The numbers on the side of each row and column indicate how many fields are to be filled in each row/column.
In a 5x5 puzzle, a "5" shows that the whole row/column has to be filled: 

      5| OOOOO

If there's more than one number at the side, it means that these 2 lines are not connected.
A "3 1" would therfor mean: 

    3 1| OOOXO

Using further thinking, more blocks can be filled.
For example, a "3" means that the line holds a line of 3 blocks. This leaves 3 possibilities:

      3| OOOXX
      3| XOOOX
      3| XXOOO

In all three cases, the one in the middle is filled, so it is safe to fill it.

Here's an example of a puzzle:

         11 11
         33033
         '''''
     22| OOXOO
      0| XXXXX
     22| OOXOO
     22| OOXOO
     22| OOXOO