F(x) is a real valued function such that:
F(x) = floor(x) +floor(10x)+floor(100x)+floor(1000x)
Determine all possible values of a positive integer N < 2016 such that:
F(x) = N has no solution for x, but:
Each of the equations: F(y) = N+11 and F(z) = N+111 has at least one solution in y and z.