Suppose a clock that is broken into four distinct pieces, that run from (12 - 9), (3-12), (6-3), (9-6). The clock can be reassembled from any two out of the four pieces, but no single piece can be used to create a full clock.
I’ve been trying to apply this idea to files and binary data, but have been having trouble finding a general formulation of the ability to take an object, divide it into multiple parts and reassemble with some portion of those parts (n out of m).
I understand that this cannot be done with only one clock. I’ve looked at Samir’s secret sharing - but I don’t think that would apply here. I’ve also spent a long time at a variety of different computer science techniques (file splitting, sharding, etc.) and I haven’t been able to find anything - so I’ve been going back to looking for a mathematical answer.
Are there general formulations of this problem? Can I use it to divide a clock into an arbitrary number of pieces (20) and then calculate how many pieces I would need to reassemble?