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Let

a\leqslant b\leqslant c

be non-negative integers. A triangle on a checkered plane with vertices in the nodes of the grid is called an

(a,b,c)

-triangle if there are exactly

a{}

nodes on one side of it (not counting vertices), exactly

b{}

nodes on the second side, and exactly

c{}

nodes on the third side.
[*]Does there exist a

(9,10,11)

-triangle? [*]Find all triples of non-negative integers

a\leqslant b\leqslant c

for which there exists an

(a,b,c)

-triangle. [*]For each such triple, find the minimum possible area of the

(a,b,c)

-triangle.
Proposed by P. Kozhevnikov

Problem Statement