The Japanese Gakken Mook series is a range of self assembly kits each with an accompanying mook (magazine-book). Kit number 26 is a particularly cool build-it-yourself miniature guitar. The kit has around 20 parts and should take an hour to put together, with the finished 4 string instrument about 15 inches long and 5 inches wide.
It has a one piece moulded plastic fretboard, tuners mounted on the body like a Steinberg and a bridge with adjustable intonation. Electronics are a single coil pickup, with an onboard amplifier and minature speaker powered by 2 AA batteries. There is also a jack socket for you to play though an external amplifier as well. The mook and kit sells for 3400 Yen ($38, £24).
Construction is fairly straight forward, mostly screwing things together. The strings, however, are anchored in a very complicated arrangement, forming almost a complete loop around the guitar. A bar is fed through the ball ends of the strings, and secured at the back of the body. The strings then go through the body and bridge, down the plastic fretboard, over the nut and back along the back of the fretboard where they are finally secured using screws, a couple of inches from where they started. Have a look at the pdf assembly instructions on Curtis Hoffman's blog.
One tricky but statisfying part is that you get build the single coil pickup yourself, winding the wire, putting in the single bar magnet and everything. It has to be a low impedance pickup, it looks like there are only a few turns around the magnet: there wouldn't be much fun in winding thousands of turns by hand.
So once you've built it what does it sound like? From what I can gather from the rash of Japanese Gakken MiniGuitar youtube videos, it sounds pretty bad. Even on the official Gakken video (see below) featuring a host of Japanese Rock and Pop stars (including Marty Friedman!) you can hear the tuning problems caused by the short scale. I think the way the strings are attached doesn't help the tuning either, there is a lot of string around the back of the neck to stretch. If I had one of these I would add a string clamping bar across the head behind the nut. Maybe tuning the thing as high as possible would help.
Having said that, I found one youtube Master of the Mini Mook Guitar: have a look at the second video. The-Bay-Wave has customised his Mini guitar, painted it red and changed the fretboard. He added his own bridge saddles, and modified the tuners with an extra bolt each. With these mods he manages to keep it in tune and stays sensisbly down the end of the neck.