Math Is Fun Forum

Hints since everyone is Not trying:
p0 substitute x(y) = ay^2 + by + c, multiply everything out, group
p1 what point inside the triangle is hardest to reach? it should be a point especially far from all sides
p2 find how many ways there are for small n
p3 inductively construct these polynomials by adding lagrange polynomials. a closed form for f(n) is unnecessary.
p4 number the road types 1,2,3,0 respectively. then a triangle is banned iff it has bitwise xor 0.