This publication describes the block winner selection process that will be used in a novel Proof-of-Useful-Work blockchain for High Energy Physics that the authors are currently working on. Instead of spamming hashing operations to mine blocks, miners will be running Monte Carlo simulations to support a real-world HEP experiment with useful data. The block problems will be defined by a Root Authority which is represented by a HEP experiment like CBM. The focus in this publication is a mechanism that allows the Root Authority to select a winner from a list of nodes that solved a block problem. The mechanism is designed so that winner selection is deterministic, fair and transparent. This mechanism allows every node to verify the fairness of the winner selection process without giving the nodes a tool to be able to improve their own winning chances.