For any positive integer n, an n-tuple of positive integers \left(x_{1}, x_{2}, \cdots, x_{n}\right) is said to be supersquared if it satisfies both of the following properties:
(1) x_{1}>x_{2}>x_{3}>\cdots>x_{n}.
(2) The sum x_{1}^{2}+x_{2}^{2}+\cdots+x_{k}^{2} is a perfect square for each 1 \leq k \leq n.
For example, (12,9,8) is super-squared, since 12>9>8, and each of 12^{2}, 12^{2}+9^{2}, and 12^{2}+9^{2}+8^{2} are perfect squares.
(a) Determine all values of t such that (32, t, 9) is super-squared.
(b) Determine a super-squared 4-tuple \left(x_{1}, x_{2}, x_{3}, x_{4}\right) with x_{1}<200.
(c) Determine whether there exists a super-squared 2012-tuple.