Line Game

Draw straight lines from each cell with a number, such that every cell in the grid contains exactly one line. The number in a cell indicates how many other cells are covered from it (not counting the cell with the number itself).


Consider the bottom 4. It must connect to four cells, but there are only three cells on the bottom row, so it must see at least one cell above it. Now, consider the cell below the 1. Since the cell to its right it connected vertically, it cannot be seen from the right anymore, so it must be connected to the 1. Now, the 1 is satisfied.

Consider the top left cell. Since the 1 is already satisfied, it must be connected to the 3. Similarly, the cell to the right of the 1 must be connected to the 4 below it, and the bottom left cell must also be connected to the same 4. The cell just below the 3 must be connected to the 3, which is then satisfied. The remaining cells must clearly be divided over the two 4s.

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