It's nuts to the shuttle, 16 to 9
Launchpad to stack connections
4 bolts with frangible nuts held each Solid Rocket Booster (SRB) to the pad.
Each solid rocket booster has four hold-down posts that fit into corresponding support posts on the mobile launcher platform. Hold-down bolts hold the SRB and launcher platform posts together. Each bolt has a nut at each end, but only the top nut is frangible. The top nut contains two NASA standard detonators, which are ignited at solid rocket motor ignition commands.
Total - 8 nuts
Picture of the nuts
SRB to External Tank (ET) connections
Each SRB had a forward attach with one explosive bolt and an aft attach with three explosive bolts.
The forward attachment point consists of a ball (SRB) and socket (ET) held together by one bolt. The bolt contains one NSD pressure cartridge at each end. The forward attachment point also carries the range safety system cross-strap wiring connecting each SRB RSS and the ET RSS with each other.
The aft attachment points consist of three separate struts: upper, diagonal and lower. Each strut contains one bolt with an NSD pressure cartridge at each end. The upper strut also carries the umbilical interface between its SRB and the external tank and on to the orbiter.
Total - 8 bolts
ET to Orbiter
The ET was structurally attached to the Orbiter by a forward attach with one explosive bolt and two aft attaches with one frangible nut each.
The forward structural attachment consists of a shear bolt unit mounted in a spherical bearing. The bolt separates at a break area when two pressure cartridges are initiated. The pressure from one or both cartridges drives one of a pair of pistons to shear the bolt, with the second piston acting as a hole plugger to fill the cavity left by the sheared bolt. A centering mechanism rotates the unit from the displacement position to a centered position, aligning the bearing flush with the adjacent thermal protection system mold line.
The aft structural attachment consists of two special bolts and pyrotechnically actuated frangible nuts that attach the external tank strut hemisphere to the orbiter's left- and right-side cavities. At separation the frangible nuts are split by a booster cartridge initiated by a detonator cartridge. The attach bolts are driven by the separation forces and a spring into a cavity in the tank strut. The frangible nut, cartridge fragments and hot gases are contained within a cover assembly, and a hole plugger isolates the fragments in the container.
The mechanical and electrical connections passed through two umbilical plates which each had three bolts equipped with frangible nuts.
The aft separation involves right and left umbilical assemblies. Each assembly contains three dual-detonator frangible nut and bolt combinations that hold the orbiter and external tank umbilical plates together during mated flight. Each bolt has a retraction spring that, after release of the nut, retracts the bolt to the external tank side of the interface. On the orbiter side, each frangible nut and its detonators are enclosed in a debris container that captures nut fragments and hot gases generated by the operation of the detonators, either of which will fracture the nut.
Total - 1 bolt, 8 nuts
Other pyrotechnic devices
I've described the explosive bolts and nuts which fired on every mission. There were a number of other non-bolt-and-nut-type pyrotechnic devices used, a few of which fired every mission (e.g. the forward landing gear thruster) but most of which were provided for contingency cases (e.g. the backup main gear deployment system, the manipulator arm jettison system, range safety, etc)
- NSD - NASA Standard Detonator
- RSS - Range Safety System
References (see each for primary sources)