  We design optimal $2 \times N$ ($2 <N$) matrices, with unit columns, so that
the maximum condition number of all the submatrices comprising 3 columns is
minimized. The problem has two applications. When estimating a 2-dimensional
signal by using only three of $N$ observations at a given time, this minimizes
the worst-case achievable estimation error. It also captures the problem of
optimum sensor placement for monitoring a source located in a plane, when only
a minimum number of required sensors are active at any given time. For
arbitrary $N\geq3$, we derive the optimal matrices which minimize the maximum
condition number of all the submatrices of three columns. Surprisingly, a
uniform distribution of the columns is \emph{not} the optimal design for odd
$N\geq 7$.
