1. The problem is to find a formula to compress a large value, possibly 100 characters or more. 2. Compression typically involves encoding data to reduce its size while preserving information. 3. One common approach is to use a hash function or a compression algorithm. 4. A simple mathematical formula to represent compression ratio is: $$\text{Compression Ratio} = \frac{\text{Original Size}}{\text{Compressed Size}}$$ 5. To compress a value mathematically, you can represent it as a function $f(x)$ that maps the original data $x$ to a smaller representation $y$: $$y = f(x)$$ 6. For example, if $x$ is a string of length $n$, $f$ could be a function that encodes $x$ into a shorter string $y$ of length $m$, where $m < n$. 7. Without specific data or method, the general formula for compression is: $$\text{Compressed Value} = f(\text{Original Value})$$ where $f$ is a compression function. 8. In practice, compression algorithms like Huffman coding, LZW, or others implement such functions. 9. Therefore, the formula to compress a large value is: $$y = f(x)$$ where $x$ is the original large value and $y$ is the compressed output.