On the issue of using “Useful” tasks for proof of works in blockchain

This paper is a logical continuation of the paper about possible approaches to solving the “Useful Proof-of-work for blockchains” problem. We suggest some alternative ways for searching useful tasks for Proof-of-work systems. These ways are based on the process of the multiple and independent repetition of a simple experiment. The experiment is to chose an element independently and uniformly from a quite large set and then to check if the chosen element has a specific rare property. In the classic blockchain of Bitcoin this experiment is a so-called hash-puzzle. In these terms the process of solving a hash-puzzle may be replaced by searching rare astronomical objects or Go positions with specific conditions. Moreover, we describe a possible attack on the blockchain systems in which the task instance generation algorithm is replaced by the algorithm of selecting the task instance from the existing database with public access for publication of task instances and discuss the way of protection.