The work done in mining a bitcoin means solving a puzzle for which there is no consistent formula. The way to find the right answer is a lot of trial and error. This is the design. There is no substitute for just running lots of numbers through the algorithm until you find one that works. And as time goes by, the number of possible combinations gets bigger, hence the more computing power is required to consistently produce solutions. Having found the answer, though, working back to check it is the right answer is very straightforward.