Guys this problem really bothers me (I don`t know how to prove it) please help:


What is the maximum number of points in convex position on a $n\times m$ grid?


(My guess would be $2\*(m+n)-4$.)



Maximum number of points in convex position on a grid
Your guess is correct. There are at most two vertical sections which contain more than 2 points. So, totally we have at most $m+m+(n-2)2=2m+2n-4$ points. The example is the perimeter of the grid.


