Greetings
I bought a used cardboard shamisen from a friend and he removed the finger locations when he re-stained the neck of the instrument. This smaller shamisen is 27 inches in length and I am not sure where the bridge goes as well distance from the wooden nut?
please, if anyone one has one of these or knows how to calculate the (finger locations) I would be soooo happy! 
The bridge is usually two or three finger widths from the bottom of the dou. You can see the placement in this video.
You can figure out the finger locations by using a tuner. (A clip-on tuner is best or you can use a tuner app on your phone.)
Tune an open (0) string to C, then find each half step along the neck: C# (1), D (2), D# (3), etc. You can use washi tape or painter’s tape to mark the positions.