Question 158
In each cell of $n \times n$ table there is an arrow pointing in one of eight principal directions (i.e. one of the following: $\rightarrow, \leftarrow, \uparrow, \downarrow, \nearrow, \searrow, \nwarrow, \swarrow$ ), in such a way that the arrows in any two adjacent cells form an angle of no more than 45 degrees, and the arrows in any two cells adjacent diagonally (i.e. sharing a vertex) form an angle of no more than 90 degrees. We start at some cell and follow the arrows (e.g. if the arrow in our cell is $\uparrow$ we move up by one, if it is $\searrow$ we move diagonally down and to the right, etc.). Prove that we will eventually escape from the table (i.e. will reach a cell on the boundary of the table where the arrow will point "out of the table").