Imagination vs Guesswork

Famously we never guess when solving Skyscrapers. But there’s a fine line between “guesswork” and “logical elimination” which I’m still unsure how to reconcile.

The question is, fundamentally, is there a difference between ‘ruling out’ a potential possibility because it results in a contradiction, and actively trying out that digit, finding it gives a contradiction, then undoing your ‘mistakes’?

In the former, you’re saying “suppose it’s this digit, then…” and this usually happens in your head.

When you start writing that hypothetical route out, it becomes more like the latter. But this feels pretty much like “we’re gonna guess this digit; if it works, happy days, if not, we’ll backtrack”.

I you ignore the question of intention, there’s no discernible difference between the two methods other than one being done in your head and the other on paper. In both you’re exploring a solution path, and then rejecting it if it isn’t correct. So why does it feel like “logic” when you do it in your head, but “guesswork” if you write it out?

At the end of the day, it just depends what your goal with solving puzzles is. I do them to have fun solving challenging problems, and having to work in my head enhances that challenge. I personally find it much more rewarding to work out the situation in my head than physically playing it out. It’s like chess.