what was the process to find the private keys when knowing the pubkeys?
As of today, there are two well-known algorithms for this process. Baby-step, giant-step, and Pollard’s rho.
EDIT: what differs known public key and unknown for getting privkeys?
In both BSGS and Pollard's rho, you need to perform operations on the elliptic curve, which requires to know the actual points involved. You can't run these algorithms based on the hash of the public key. And since both have time complexity O(sqrt(N)), you have an orders of magnitude advantage on working out private keys of known pubic keys.
You can not find a private key from a public key just like can not find a public key from a public address.
You can actually perform a reversal from public key to private by reversing the modular multiplications which produced the public key; it's just very computationally expensive, and considered infeasible for very long numbers like 256 bits. In mentioned puzzles, the puzzle makers have deliberately generated insecure keys, to encourage finders from attempting to break them. It's a smart way to know the progress in breaking the elliptic curve's security.
What are these puzzles you are refering to?
They're probably referring to these:
https://bitcointalk.org/index.php?topic=5218972.0.
Here's a good article for everyone interested in the details to read:
https://andrea.corbellini.name/2015/06/08/elliptic-curve-cryptography-breaking-security-and-a-comparison-with-rsa.
