Rating Difficulty

Agent Allen · Posted: Sun Oct 02, 2005 6:49 pm Post subject: absolutely

You said:

Chigger · Posted: Thu Oct 06, 2005 7:53 pm Post subject:

Ruud · Site Admin

Agent Allen

Ruud - great gagging Laughing

Seriously there seems to be a lot of concenus on using 'techniques' like hidden singles, naked singles , subsets and so on in various measure resorting to brute force if you run out of tricks.

Its probably correct that because the easier techniques are computationally cheap, you should exploit all the easys then resort to a toughie, then go back for any now revealed easys, resorting to toughy after that and so on.

That seems sensible and most sudokorists I've spoken to certainly take that approach themselves.

I think both Howard and Chigger may be on to something that the number of options and when in the solving they arise (or must arise) might have a significant effect on difficulty.

I seems to me - though I haven't had time to actually produce an example (anybody?) - that even at a trivial level how many features you find might be a matter of where you look.

Suppose you solve all naked singles and are left with 2 hidden singles.
Taking one reveals a naked and that cascades to reveal the other hidden.
However the other one, say reveals nothing and you're forced to find and solve the other.
So in 'attempt' you're counting n+1 naked and 1 hidden. In another n naked and 2 hidden. Whose right?

Both approaches may be similar on the space of all puzzles but stumble on different moves first, take the bird in the hand and move on...
As mentioned that appears to be a valid human and machine approach.

However grading puzzles differently depending on how you 'can' the blocks seems wrong to me.
It should be an intrinsic property of the puzzle not an arbitrary artifact of the for loops. Humans have a quick wander, where as computers tend to start top left but might go rows, columns, houses or houses, columns, rows.

Now a clever machine or human might be able to spot the 'potent' hiddens better than another. It might not be entirely coincidence that the first solver revealed some naked singles.

It may be that to evaluate difficulty you need to look at all solve paths (or all reasonable ones) and somehow rate an average off the back of them.
It may be effective or ineffective to bestow 'intuition' (judgement) on the human player and calculate an average where the shorter "solves" are more likely.

Who knows?

I was told by a faster sudokrist than me that going for a trial and error near the edge of the game was a worse move than a trial and error in a cell with the same number of candidates but in the middel cell.
In the puzzle in hand they ended up with 1 trial and error episode and I had 2. It was rated very difficult, but perhaps no as difficult as I made it.

So on that day it worked for them...

On the face of it they might look lucky, but they're making their own luck (maybe) or bulls**tting me - I still don't really know.

This leads you to a whole variety of possible measures:

Least weighted solve pattern.
Reverse Lexicographically first solve pattern (least on hardest...to least on smallest).
Averaged solve pattern.
Weight average solve pattern.

For me to determine a 'betterness' between all these (and any you might have) methods of grading difficulty, you still need an objective definition of difficultly.

But thats getting back to my broken record:

Err guys what do you mean by more or less difficult, specifically?
Difficult for whom and in what way would that be?

All the measures discussed are [trivially] a solution to working out the number they calculate, but what use are those numbers and what do they tell us?

I want them to tell me if I can finish the puzzle in an 1 hour or not or tell me if I finish this in under 30 minutes I rock...
How about you?
_________________
Agent A

Chigger

Agent Allen · Posted: Sun Oct 09, 2005 7:08 pm Post subject: Thanks for the input

Chigger,

Thanks for the anecdotal testimony. I think its useful stuff to circulate.
I know the sorts of processes I go through when trying to do a puzzle, but without a body of this sort of testimony its impossible to know if personal approaches are at all general.
Your description sounds familar to me in my experience solving puzzles.
I wonder how much resonance it has for others.
Could you publish one of the puzzles you've solved by different routes?

So to your analysis of your testimony: