If a convex lattice polygon has I 1, we might expect to find an inequality of the form BI + k?
True ; False
False. The long rectangles of width 2 show that there are polygons for which B increases faster than I.
2.
If a convex lattice polygon has I 1, we might expect to find an inequality of the form B 3I + 6?
True ; False
True – perhaps! The right triangle with I = 1 has B = 9, so we obtain equality in this case. This is only a conjecture; it is almost certainly true but has not been proved.
3.
There exists a convex lattice pentagon with I = 0.
True ; False
False. This result of Erdös is a surprising result.
4.
There is a unique lattice triangle with B = 9 and I = 1.
True ; False
False. There is an infinite family of equivalent triangles: triangles which have 4 lattice points on each side. For example, we have a triangle with vertices O, (3, 0), and (3, 3), and another triangle with vertices O, (3, 3), (3, 6), obtained from the first by a shear.
5.
The smallest number of interior points contained by a convex hexagon is 2.
True ; False
False. It is easy to find a hexagon containing just one interior point.
6.
There is an inequality for convex lattice polygons which gives a lower bound for B in terms of I.
True ; False
True, but the result is trivial. For any value of I, we can find a triangle with I interior points and B = 3 (0I + 3). Put the points on a horizontal lattice line. For example if I = 3, and the interior points are (1, 1), (1, 2), (1, 3), a triangle could have vertices O, (4, 1), (1, 2).
1, we might expect to find an inequality of the form 
I + k?