ILL 1984 Problem 56

Let $a, b, c$ be nonnegative integers such that $a \le b \le c, 2b \neq a + c$ and $\frac{a+b+c}{3}$ is an integer. Is it possible to find three nonnegative integers $d, e$ , and $f$ such that $d \le e \le f, f \neq c$ , and such that $a^2+b^2+c^2 = d^2 + e^2 + f^2$ ?