Create randomly-generated image grids in InDesign?

Hello all! 

I'm hoping that someone can help me figure out how to create a set of lotería tablas (similar to bingo) using a set of 54 images distributed randomly across 100 pages.

Requirements:

• 100 total pages, each with one grid
• Image grids will be 4x4
• Each page must have a unique arrangement of images
• Any one image should be used only once on each page
• Spacing and placement of the grid must be consistent across all pages.

I have a notion that this could be solved using scripts, but I have almost no experience with creating or using those myself. Any help would be appreciated!

I have attached an example of how I'd like for these tablas to be laid out for your reference. Happy to answer any questions you may have if it helps me get to a solution!