What are the math problems in Bitcoin mining? [Examples]

What are the math problems in Bitcoin mining? [Examples]

Robert McDougall 

June 1, 2023


Key Takeaways

  • Bitcoin mining is the process of solving complex mathematical equations and hash puzzles to validate Bitcoin transactions and reduce the risk of fraudulent activities.
  • Blockchain technology is the digital ledger where every transaction is recorded, and blocks are used to store the details.
  • The three common mathematical problems in Bitcoin mining are hashing, double-spending, and the Byzantine General Problem.

If you have been trying to wrap your head around what Bitcoin mining is and how exactly it works in the real world, know that you are not alone in trying to understand the whole scenario. If you have done a little research, you might already know that Bitcoin mining consists of solving complex mathematical equations and hash puzzles by using the computational power you provide through your hardware. It is simply done to validate the Bitcoin transactions on the network and reduce the risk of fraudulent activities and invalid transactions that could affect the whole network.

But the question is, why solve mathematical problems that require a massive amount of computational power to solve a single block on the network? Why are they so complex and can’t be solved typically? Are those mathematical problems quantum equations that might bring a revolution to humankind and change the way we live? Or is there a disappointing answer to this question that you might not want to hear? Let’s take a deep dive into the details and find out what the math problems in Bitcoin mining are.

Taking a look into Blockchain: What’s the fuss about?

Before we take a look and understand math problems in bitcoin mining, it is important to understand what blockchain is and why it is talked about so much when it comes to cryptocurrencies. Blockchain is the structure or technology that Bitcoin is based on. Blockchain can also be considered as a digital ledger where every single thing is recorded, including all the transactions on the network. 

When it comes to storing data, blockchain technology uses blocks to store the details. And every block contains nonce, hash, and data to store a value or a particular set of information regarding the transactions. 

What are mathematical equations in Bitcoin mining?

So the first thing that you should keep in mind when evaluating mathematical equations in Bitcoin mining is that we are not talking about the usual equations we tend to use in our daily lives. Here, we are talking about algorithms that are specifically designed for validation of the transactions that help the network verify pretty much everything.

For context, Bitcoin mining uses the SHA-256 algorithm, which produces and carefully assigns a hash to every single Bitcoin transaction that is being processed on the blockchain. Of course, every hash that is being produced by the algorithm is unique and does not ever repeat on the blockchain. In case of any fraudulent activity on the network, or any attempt to tamper with the hashes assigned to the transactions, the network rejects it instantly as it does not find it in the record of the SHA-256 algorithm. 

What does it mean to solve puzzles in Bitcoin mining?

Another popular terminology that you might have come across when exploring Bitcoin mining is “puzzles.” What are these puzzles and how are they relevant when it comes to mining Bitcoin? Well, miners have to solve the puzzles that again follow the mathematical structure in order to provide proof of work and contribute to validating the transactions on the network. 

Also, puzzles help miners solve a particular hash that comes with its own mining difficulty. The mining difficulty of a hash can be determined by the number of miners competing with each other to solve it. Do remember that it solely depends on the efficiency of your mining hardware that how much time it would take to solve a puzzle and find a hash.

What role does proof-of-work play in mining?

There is one interesting thing about cryptocurrencies, and of course Bitcoin, that impressed people right from the start. And that thing is, Bitcoin and other crypto assets are decentralized without an organization managing the crucial things. However, when it comes to decentralization, security and privacy leave a big question mark and make people question the credibility of the project. To solve that problem, the proof-of-work mechanism was introduced to the blockchain industry, which has been followed for more than a decade now.

Just like the name of the mechanism suggests, proof-of-work simply uses the computational power provided by the miners to make the whole system authentic and legitimate. Proof-of-work is what verifies the transactions and keeps everything in check to eliminate the risk of fraud. In other words, it is a mechanism that allows the world to see how secure the blockchain industry is and how computational power can provide security and safety to your transactions. 

The three common mathematical Bitcoin mining problems

By now, you should have a broad idea about how Bitcoin mining works and what is the role of mathematical problems in Bitcoin mining. But it is also interesting to know exactly the types of mathematical problems that are being solved when mining Bitcoin. Take a look below and find out for yourself:

  • Hashing: Hashing is the most common mathematical problem used in Bitcoin mining. Each hash contains a header consisting of data and a puzzle to be solved by the miner. 
  • Double-spending: Although this mathematical problem is not very common, it still happens in the blockchain industry. Double-spending refers to digital currencies that are spent twice. This problem can occur due to different circumstances but can be easily solved by the proof-of-work mechanism led by any miner.
  • Byzantine General Problem: Byzantine general problem occurs when miners creating new blocks try to put them at the same spot simultaneously. Due to this, confusion can be created as to which block from the two would be approved on the Blockchain and enter the system. This whole scenario depends on the majority of the miners on the network and which of the block they would accept. If the block has a winning percentage of 51%, it will be accepted.


I know it can be a little challenging to understand everything mentioned above, especially if you are not tech-savvy, but don’t worry, your experience exploring the industry will help you over time. You can read through the article again, learn how it all works, and what are the complexities behind the Bitcoin mining procedure. If you are interested in mining Bitcoin, you can take a look at our article on how to join a mining pool, or learn how to build your own ASIC miner.

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