What special math trick of a hash function helps make sure blockchain data has not been secretly changed?

The special mathematical trick of a hash function that helps ensure blockchain data has not been secretly changed is its ability to create a unique, fixed-size digital fingerprint for any piece of data, combined with several key properties that make this fingerprint tamper-evident. A hash function is a mathematical process that takes an input of any size and transforms it into a string of characters of a predetermined, fixed length, called a hash or digest. For example, the word "hello" might produce a hash like "2CF24DBA5FB0A30E26E83B2AC5B9E29E1B161E5C1FA7425E73043362938B9824," regardless of whether the input was one word or an entire book.
The core properties that make this trick effective are:
First, it is a one-way function, meaning it is computationally infeasible to reverse the process and derive the original data from its hash. You can go from the data to the hash, but not back from the hash to the data.
Second, it is deterministic, which means that the exact same input data will always produce the exact same hash output. If the data hasn't changed, its hash will always be identical.
Third, it exhibits the avalanche effect. Even a tiny alteration to the input data, such as changing a single character or number, will result in a completely different and unpredictable hash output. This makes even subtle modifications immediately obvious, as the new hash will bear no resemblance to the original.
Fourth, it possesses collision resistance. It is extremely difficult, to the point of being practically impossible, to find two different pieces of input data that produce the exact same hash output. This ensures that each unique set of data has a virtually unique digital fingerprint.
In a blockchain, each block contains not only its own data (like transaction records) but also the hash of the *previousblock. The current block's own hash is calculated by taking *allof its contents, including the hash of the previous block, and running them through the hash function. This creates a secure chain where each block is cryptographically linked to the one before it. If someone attempts to secretly alter any data within an old block, the hash of that specific block will immediately change due to the avalanche effect. Because the subsequent block in the chain was calculated using the *originalhash of the now-altered block, the stored hash in the next block will no longer match the newly calculated hash of the changed block. This discrepancy breaks the chain's integrity, making any unauthorized modification instantly detectable by anyone verifying the sequence of hashes. The entire chain of blocks becomes invalid from the point of alteration onward, thereby ensuring that blockchain data has not been secretly changed.