  We show that the supergravity solutions for 1/4-BPS intersecting systems of
M2 and M5 branes are completely characterized by a single ``maze'' function
that satisfies a non-linear ``maze'' equation similar to the Monge-Amp\`ere
equation. We also show that the near-brane limit of certain intersections are
$AdS_3 \times S^3 \times S^3$ solutions warped over a Riemann surface,
$\Sigma$. There is an extensive literature on these subjects and we construct
mappings between various approaches and use brane probes to elucidate the
relationships between the M2-M5 and AdS systems. We also use dualities to map
our results onto other systems of intersecting branes. This work is motivated
by the recent realization that adding momentum to M2-M5 intersections gives a
supermaze that can reproduce the black-hole entropy without ever developing an
event horizon. We take a step in this direction by adding a certain type of
momentum charges that blackens the M2-M5 intersecting branes. The near-brane
limit of these solutions is a BTZ$^{extremal} \times S^3 \times S^3 \times
\Sigma$ geometry in which the BTZ momentum is a function of the Riemann surface
coordinates.
