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Hard puzzle
MrTheMan
Kwon-Tom Obsessive
Puzzles: 647
Best Total: 17m 29s
Posted - 2006.05.30 23:05:29
I just wanted to know for the new software I am creating if there is any possibility anybody could solve a puzzle this hard;

mathmaniac
Kwon-Tom Obsessive
Puzzles: 1198
Best Total: 20m 57s
Posted - 2006.05.30 23:11:46
I'll give it a shot. Maybe foilman could show it to his puzzle creator.
m2e
Kwon-Tom Obsessive
Puzzles: 607
Best Total: 16m 43s
Posted - 2006.05.30 23:19:57
I'll try too. PLease keep us posted on your software!
foilman
Kwon-Tom Admin
Puzzles: 1720
Best Total: 24m 8s
Posted - 2006.05.30 23:35:18
My puzzle creator gives up fairly early on trying to solve this! It only manages to put 14 lines in place... are you sure there's only one possible solution?

Edit: re-ran it and solved it... see my post further down...
Last edited by foilman - 2006.05.31 08:19:59
m2e
Kwon-Tom Obsessive
Puzzles: 607
Best Total: 16m 43s
Posted - 2006.05.30 23:39:29
well its took me 19 mintutes and i *think* i have the answer. do i post it here or what?
m2e
Kwon-Tom Obsessive
Puzzles: 607
Best Total: 16m 43s
Posted - 2006.05.30 23:40:02
But yeah i'm not sure if i have the ONLY answer
foilman
Kwon-Tom Admin
Puzzles: 1720
Best Total: 24m 8s
Posted - 2006.05.30 23:43:53
If you're logged in to the site, this will display the puzzle for you to have a go at (and you can even submit your solution now too!)

The Hard Puzzle
Last edited by foilman - 2006.05.31 09:40:51
m2e
Kwon-Tom Obsessive
Puzzles: 607
Best Total: 16m 43s
Posted - 2006.05.31 00:15:55
**spoiler**
My answer here
mathmaniac
Kwon-Tom Obsessive
Puzzles: 1198
Best Total: 20m 57s
Posted - 2006.05.31 02:22:34
I'm glad someone managed to complete it. I gave up!
Erick
Kwon-Tom Obsessive
Puzzles: 1292
Best Total: 31m 39s
Posted - 2006.05.31 03:58:57
I'm reasonably sure it's unique.  It wasn't easy, but I think I covered all the possibilities.
prj
Kwon-Tom Obsessive
Puzzles: 2356
Best Total: 18m 20s
Posted - 2006.05.31 05:21:18
I've also worked out the same solution, and unless I made a mistake, it is unique.  Still, I'm glad we don't have to deal with puzzles that hard every week.
procrastinator
Kwon-Tom Obsessive
Puzzles: 1083
Best Total: 12m 56s
Posted - 2006.05.31 07:35:08
This can be solved very easily using Fix Position - if you guess the right thing you get all the way to the end. I can't yet see how to rule out the other alternative to solve it without FP, but the thing I guessed was one of the most obvious things to try, so I'd expect normal Friday scores on average but with more than normal variation.
astrokath
Kwon-Tom Obsessive
Puzzles: 3093
Best Total: 13m 42s
Posted - 2006.05.31 07:55:43
I completed that way too, but I'm not yet convinced it's unique.
procrastinator
Kwon-Tom Obsessive
Puzzles: 1083
Best Total: 12m 56s
Posted - 2006.05.31 08:10:14
Quote:
Originally Posted by astrokath
I completed that way too, but I'm not yet convinced it's unique.

I went through it again and trying not to use any uniqueness arguments, and I'm pretty sure I succeeded.
foilman
Kwon-Tom Admin
Puzzles: 1720
Best Total: 24m 8s
Posted - 2006.05.31 08:15:52
Yes, that is the one and only solution, but it's a tough one to prove! I re-ran my puzzle creator in "deep analysis" mode and it solved it ok this time... but took ages! Most daily puzzles get an internal score from 1 (very easy) to a maximum of around 10ish (very hard)... this one scored 43!!!! So don't expect to see similar ones appearing here...
procrastinator
Kwon-Tom Obsessive
Puzzles: 1083
Best Total: 12m 56s
Posted - 2006.05.31 08:59:11
Quote:
Originally Posted by foilman
Most daily puzzles get an internal score from 1 (very easy) to a maximum of around 10ish (very hard)... this one scored 43!!!!

If you don't mind me prying on a fascinating topic: do you do two phases, one for uniqueness and one for difficulty, or do you just not use any uniqueness-dependent patterns in your difficulty function?

My guess is that to prevent inflation of difficulties, you haven't added any new patterns (or guessing heuristics) since you started the site - so perhaps you didn't even know any uniqueness patterns when you wrote it.

On the other hand course this (and whatever other new-found patterns your program doesn't know) means less (and perhaps decreasing) consistency between your ratings and our times. This puzzle would be a significant outlier - there have certainly been (subjectively) harder Friday puzzles that your algorithm rated as reasonable.

I also wonder whether you use least-depth, average-depth (I don't imagine you can search the whole space of guess-orderings, but you could sample randomly or prune the choices either heuristically or by least immediate consequences, right?), or some combination? Because you'd probably also find we get closer to least and further from average as our intuition improves about where to make our guesses.

And should adding two adjacent edges on a 3 count as depth 1 or 2, or somewhere in between?
foilman
Kwon-Tom Admin
Puzzles: 1720
Best Total: 24m 8s
Posted - 2006.05.31 09:12:18
Quote:
Originally Posted by procrastinator
If you don't mind me prying on a fascinating topic: do you do two phases, one for uniqueness and one for difficulty, or do you just not use any uniqueness-dependent patterns in your difficulty function?
There aren't any uniqueness-dependent patterns in my algorithms, because it uses the same code to create the puzzles, and at that point I don't know if there's a unique solution or not. It's basically solving the puzzles exactly the same way I do (minus uniqueness), so the difficulty is really how difficult I find the puzzles!!! (99% of the time, anyway)

Quote:
Originally Posted by procrastinator
My guess is that to prevent inflation of difficulties, you haven't added any new patterns (or guessing heuristics) since you started the site - so perhaps you didn't even know any uniqueness patterns when you wrote it.
I've added one or two, hence why if you look back at the early archives some puzzles have changed ratings, but it's basically the same.

Quote:
Originally Posted by procrastinator
On the other hand course this (and whatever other new-found patterns your program doesn't know) means less (and perhaps decreasing) consistency between your ratings and our times. This puzzle would be a significant outlier - there have certainly been (subjectively) harder Friday puzzles that your algorithm rated as reasonable.
I found this one very tricky, so obviously for me it's still rating them correctly.
procrastinator
Kwon-Tom Obsessive
Puzzles: 1083
Best Total: 12m 56s
Posted - 2006.05.31 09:16:01
Quote:
Originally Posted by foilman
It's basically solving the puzzles exactly the same way I do (minus uniqueness), so the difficulty is really how difficult I find the puzzles!!! (99% of the time, anyway)

Small wonder you're Mr. Consistent.
foilman
Kwon-Tom Admin
Puzzles: 1720
Best Total: 24m 8s
Posted - 2006.05.31 09:20:56
And anyway my algorithm is more interested in puzzles that have some kind of symmetry (rotated, reflected etc) than ones that are difficult to solve. Hehe.
MrTheMan
Kwon-Tom Obsessive
Puzzles: 647
Best Total: 17m 29s
Posted - 2006.05.31 09:26:00
For the ones that don't believe it, trust me, there is only one solution.

Now about my software. I would already have released it if my company's domain wouldn't have given up on us (it should be back soon though). Maybe some of the people here on the forum could be beta testers though, so that I can find any bugs before I release the software.

Some features:

- Auto generates puzzles at any difficulty and of sizes up to 50x50 (by clicking auto-generate, by drawing a line and generate the numbers for it or by drawing the numbers yourself)
- Hint system that works for easy puzzles
- It will rate the puzzles with a difficulty, but since I don't know how this website rates puzzles the rating system is different.
- Some tutorials (there should be more in the future)
- Integrated timer

So tell me if any one of you is interested in testing the software
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