Measuring thousands of sensors using a single board

Hello everyone,

I initially developed a system based on Arduino where I could measure 6 resistors sequentially and basically ascertain whether they were there or not. So infinite resistance basically meant 'no resistor'. This way I could tract the presence, absence and misplacement of resistors. This was not very hard to do. Now here is the problem -

I have to scale this exact system to one that measures thousands of resistors (50,000 as of now), ascertains whether each is in its place or...

Measuring thousands of sensors using a single board