Depending on how sequential the serial numbers are, the answer (the probable range of serials) can probably be derived either from people reporting true serial

Depending on how sequential the serial numbers are, the answer (the probable range of serials) can probably be derived either from people reporting true serial + some random noise offset (of known distribution), or maybe through some zero-knowledge protocol (but I don't know if zero-knowledge proofs are practical on a many-party scale).