I count 5 if the rack off to the right of the second picture has a set of speakers attatched. I base the designation "rig" on the number of transducers. A set of ESL-57 with a choice of 3 racks, one containing Quad, one containing Naim and one containing Technics, I would consider one big rig.
The Quad rack with a choice of ESL-57s, MMGs, Acoustimass or B&W as transducers, is 4 rigs.
But thats just me.
(Pimp rigs btw )