  For some m \ge 4, let us color each column of the integer lattice L = Z^2
independently and uniformly into one of m colors. We do the same for the rows,
independently from the columns. A point of L will be called blocked if its row
and column have the same color. We say that this random configuration
percolates if there is a path in L starting at the origin, consisting of
rightward and upward unit steps, and avoiding the blocked points. As a problem
arising in distributed computing, it has been conjectured that for m \ge 4, the
configuration percolates with positive probability. This has now been proved
(in a later paper), for large m. Here, we prove that the probability that there
is percolation to distance n but not to infinity is not exponentially small in
n. This narrows the range of methods available for proving the conjecture.
