If you just want continuity, then you can join them all at one end, and then you only need a one-to-50 at the other end. But you probably want to know about shorts, too.
type of shift registers or multiplexers
So just use the little search box (top right on every page) on this forum for "shift registers
" or "muliplexers
" and you get plenty of ideas from others who have done it before and already written about it
. If you have specific question ask them in the LED and Multiplexing
As for the project in general : Yes, enough 1-to-8 multiplexers to get your 100 lines, and a simple program with two nested loops (to test every-one-against-every-other wire should do it. Hint: You set all pins to HIGH on the one side of the cable, except one to LOW. Then you probe for the LOW one on the input side. By using the internal pullup resistor no more parts are needed. (I did a 15 minute program for working out a weird thumbwheel switch I picked up as junk. It only had 8 leads, so I did not need a shiftregister). Your program only needs to write the unexpected result, and you can save the LCD by using the Serial/USB/computer (unless you wnat a standalone test box)