The present dissertation addresses the problem of fairly distributing shared resources in non-commercial blockchain networks. Blockchains are distributed systems that order and timestamp records of a given network of users, in a public, cryptographically secure, and consensual way. The records, which may in kind be events, transaction orders, sets of rules for structured transactions etc. are placed within well-defined datastructures called blocks, and they are linked to each other by the virtue of cryptographic pointers, in a total ordering which represents their temporal relations of succession. The ability to operate on the blockchain, and/or to contribute a record to the content of a block are shared resources of the blockchain systems. In commercial networks, these resources are exchanged in return for fiat money, and consequently, fairness is not a relevant problem in terms of computer engineering. In non-commercial networks, however, monetary solutions are not available, by definition. The present non-commercial blockchain networks employ trivial distribution mechanisms called faucets, which offer fixed amounts of free tokens (called cryptocurrencies) specific to the given network. This mechanism, although simple and efficient, is prone to denial of service (DoS) attacks and cannot address the fairness problem. In the present dissertation, the faucet mechanism is adapted for fair distribution, in line with Max-min Fairness scheme. In total, we contributed 6 distinct Max-min Fair algorithms as efficient blockchain faucets. The algorithms we contribute are resistant to DoS attacks, low-cost in terms of blockchain computation economics, and they also allow for different user weighting policies.