  We propose a new Ising spin glass model on $Z^d$ of Edwards-Anderson type,
but with highly disordered coupling magnitudes, in which a greedy algorithm for
producing ground states is exact. We find that the procedure for determining
(infinite volume) ground states for this model can be related to invasion
percolation with the number of ground states identified as $2^{\cal N}$, where
${\cal N} = {\cal N}(d)$ is the number of distinct global components in the
``invasion forest''. We prove that ${\cal N}(d) = \infty$ if the invasion
connectivity function is square summable. We argue that the critical dimension
separating ${\cal N} = 1$ and ${\cal N} = \infty$ is $d_c = 8$. When ${\cal
N}(d) = \infty$, we consider free or periodic boundary conditions on cubes of
side length $L$ and show that frustration leads to chaotic $L$ dependence with
{\it all} pairs of ground states occuring as subsequence limits. We briefly
discuss applications of our results to random walk problems on rugged
landscapes.
