Ajò Dimonios wrote:Hi Denis

Denis wrote:

The puzzle can be solved with chains of length 4.

Surely if we interpret the difficulty of a puzzle, the length of the longest whip present in the resolution, I agree with you. But if we also consider the number of whips and other logical steps, we should multiply the length of these by the number of whips. For a human solver it is not the length of the single logical chain that determines the difficulty but the total number of single simple logical steps that lead to the solution. It must also be considered that once a mechanism has been triggered, albeit long, it is a question of applying simple rules (singles, allignaments and only rarely naked and hidden), while, always for a human solver, the search for another whip valid after having concluded positively one certainly has a certain difficulty.

Hi Paolo

For the main points, see my answer to Robert.

SudoRules applies simplest-first search. I always said that a human solver would not be so systematic.

SudoRues doesn't try to minimise the number of steps. Some steps are not necessary. I'm sure François would find a simpler path with whips no longer than 4.

As for your idea of defining difficulty as a total number of steps, it makes no sense. All the elementary steps are obvious. But they are not all useful. So, using useful steps / total possible steps would be more realistic.

However, there are three problems with definitions based on the total number of steps:

- they allow no theoretical analyses. That's why the theoretical content of Robert's approach is close to null.

- they can't take every step into account in consistent ways. If you don't count singles (let alone elementary eliminations) appearing at the top level, why would you count them when you use them within your double T&E procedure?

- how do you count the cost of comparing the two or three branches of T&E? (especially as you don't keep track of the eliminations)