Question 18
The plane was divided by vertical and horizontal lines into unit squares. Determine whether it is possible to write integers into cells of this infinite grid so that:
(i) every cell contains exactly one integer
(ii) every integer appears exactly once
(iii) for every two cells $A$ and $B$ sharing exactly one vertex, if they contain integers $a$ and $b$ then at least one of the cells sharing a common side with both $A$ and $B$ contains an integer between $a$ and $b$.
(i) every cell contains exactly one integer
(ii) every integer appears exactly once
(iii) for every two cells $A$ and $B$ sharing exactly one vertex, if they contain integers $a$ and $b$ then at least one of the cells sharing a common side with both $A$ and $B$ contains an integer between $a$ and $b$.