  We consider the one-dimensional target search process that involves an
immobile target located at the origin and $N$ searchers performing independent
Brownian motions starting at the initial positions $\vec x = (x_1,x_2,...,
x_N)$ all on the positive half space. The process stops when the target is
first found by one of the searchers. We compute the probability distribution of
the maximum distance $m$ visited by the searchers till the stopping time and
show that it has a power law tail: $P_N(m|\vec x)\sim B_N (x_1x_2...
x_N)/m^{N+1}$ for large $m$. Thus all moments of $m$ up to the order $(N-1)$
are finite, while the higher moments diverge. The prefactor $B_N$ increases
with $N$ faster than exponentially. Our solution gives the exit probability of
a set of $N$ particles from a box $[0,L]$ through the left boundary.
Incidentally, it also provides an exact solution of the Laplace's equation in
an $N$-dimensional hypercube with some prescribed boundary conditions. The
analytical results are in excellent agreement with Monte Carlo simulations.
