The name of the most famous cryptographic hashing function is arguably SHA-256. The function defines exactly what mathematical expressions are applied to get a nearly perfectly untraceable output to a given input. (Meaning no way to strategically figure out what input caused the output). So, when you say ‘solve’ most mathematicians would think of an equation with some variable. They rearrange to get the variable by itself and then they know its value… This is not what is happening in mining. In mining, they guess a number, send it through SHA-256 and see if the result looks the way they want it. No solving, just guess and check.
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