The statement in question N describes it as first-degree polynomial, but it is precisely the first-degree or less polynomial that is given.
Statements of Problem E
The original statement of problem E misses an important condition that $|a-c| + |b-d|$ should be exactly $1$. Now it has been fixed. Please refresh the statements.
Additional example on problem
The third example of problem F was missing. Now it has been fixed.