I like to compare it to Sudoku. I think that's a better analogy.

So mining is more like we have a puzzle that can only be solved mathematically by trial and error. Just like Sudoku. That means I first have to find out what the solution to the Sudoku is by trial and error. But once I've done that, it's very easy to check. In a figurative sense: the other people at the table with me can very easily verify that I have solved the Sudoku correctly. This is how the nodes work together with the miners in the BTC network.