Making mistakes better

I have been playing Sudoku again. When I first learned to do the puzzles, I thought that the point was never to make a move that you were not certain was right. Many of the puzzles I did were constructed that way: there was always at least one right move, however hard it was to spot, and each right move would lead to the next until the puzzle was complete.

Then I started doing harder puzzles. And I learned that, at least in some books, there was a point in each of the harder puzzles where there was no way to know the right answer. The best strategy seemed to be to use what was knowable to narrow the puzzle as far as possible and then to guess and see what happened.

The faster you make a mistake, the faster you can correct and find the answer.

Often, the right answer unlocks the rest of the puzzle relatively effortlessly. But sometimes, this will also seem to be true of the wrong answer. One after the other, the answers appear until, suddenly, it becomes clear that you've taken the wrong path. There are too many of some numbers and not enough of others.

At this point, because it is a game completed for enjoyment, you have two options. You can quit and go on to a fresh puzzle. Or you can retrace your steps and make a different choice without regret or hesitation. Your new choice might or might not unlock the whole of the solution.

The faster you get used to making mistakes, the more puzzles you can solve.