| Fri. July 21 (Friday, 21st July 2006) |
PuzzleLover
Kwon-Tom Obsessive
Puzzles: 1033
Best Total: 38m 17s | Posted - 2006.07.24 00:33:38
How does one proceed from here in last Friday's puzzle? When I solved it, I made painfully slow progress with guesses (most were inconclusive) and Fix Position. E.g., a Fix Position beyond my reading skills rules out left+bottom around the 3 @ r8c4.
Can tractable logic or simple reading make any more progress? Thanks.
Note in edit: I accidentally left out a 2 @ r2c3. I'll leave it out, since it created an interesting Highlander situation and an example of a "good" puzzle with a globally unique solution with a limited local non-uniqueness. Discussions below find the globally unique solution even with the 2 left out, whereas a Highlander "deduction" cannot be extended to any solution.
Last edited by PuzzleLover - 2006.07.24 03:30:25 |
PuzzleLover
Kwon-Tom Obsessive
Puzzles: 1033
Best Total: 38m 17s | Posted - 2006.07.24 02:24:31
A comment / question on this puzzle before the position in the first message is reached. The upper middle starts
I explored how to get by the upper 1 (above or right). Right doesn't work, but I needed a long Fix Position extending into the upper left corner to see this. Are there better deductions available, or is this a clear early choice to try? |
m2e
Kwon-Tom Obsessive
Puzzles: 607
Best Total: 16m 43s | Posted - 2006.07.24 02:32:30
Quote: Originally Posted by puzzlelover How does one proceed from here in last Friday's puzzle? When I solved it, I made painfully slow progress with guesses (most were inconclusive) and Fix Position. E.g., a Fix Position beyond my reading skills rules out left+bottom around the 3 @ r8c4. Can tractable logic or simple reading make any more progress? Thanks. |
I made a move at the top left as shown there. It is because otherwise there would be 2 possible answers |
PuzzleLover
Kwon-Tom Obsessive
Puzzles: 1033
Best Total: 38m 17s | Posted - 2006.07.24 02:53:54
Here are a series of Fix Position attempts with conclusions that led to a solution. They're mostly guesses that worked, which followed many other inconclusive guesses.
Can anyone suggest better guesses or non-guesses?
1. 3 @ r8c4 needs top + right -- bottom + left leads to a loop.
2. 3 @ r8c4 needs left -- bottom leads to isolated end - I can't quite read it though.
3. 2 @ r10c4 needs bottom -- else dangling end - also beyond my reading skills.
If you're lucky or smart enough to find these choices to try, the puzzle falls into place after counting endpoints areound the 3 @ r3c5. But how do you find good places to try??? |
PuzzleLover
Kwon-Tom Obsessive
Puzzles: 1033
Best Total: 38m 17s | Posted - 2006.07.24 03:23:19
Quote: Originally Posted by m2e I made a move at the top left as shown there. It is because otherwise there would be 2 possible answers |
I accidentally omitted the 2 @ r2c3 in my initial post. Doing so gives an interesting puzzle (and a good puzzle, in my opinion). The puzzles has exactly 2 solutions, which are the variations the Highlander "deduction" makes unique. Note that the two Highlander variations are minor local variations in an otherwise globally unique solution.
If you make the Highlander "deduction", it does not extend to a solution.
Last edited by PuzzleLover - 2006.07.24 03:34:41 |
m2e
Kwon-Tom Obsessive
Puzzles: 607
Best Total: 16m 43s | Posted - 2006.07.24 04:17:22
inserted 3 more lines in the bottom left that i could see without fix position. I only did the first move of these, not following them up so they might open more possibilities. |
PuzzleLover
Kwon-Tom Obsessive
Puzzles: 1033
Best Total: 38m 17s | Posted - 2006.07.24 08:05:03
Quote: Originally Posted by m2e inserted 3 more lines in the bottom left that i could see without fix position. I only did the first move of these, not following them up so they might open more possibilities. |
and inspires related pattern (Edit: oops, not a pattern, see below)
With these observations and my reading skills, I can solve this puzzle without Fix Position except for the 1 in the upper middle. Thanks!
Last edited by PuzzleLover - 2006.07.25 22:18:08 |
drnull
Kwon-Tom Obsessive
Puzzles: 1053
Best Total: 23m 25s | Posted - 2006.07.25 12:19:48
Quote: Originally Posted by puzzlelover and inspires related pattern |
?? |
Acorn
Kwon-Tom Obsessive
Puzzles: 555
Best Total: 42m 58s | Posted - 2006.07.25 18:51:10
I don't get it? Can someone explain why a single "x" near a three means anything? I can't even figure out how you got these lines in near the threes. This Friday puzzle almost killed me. |
mathmaniac
Kwon-Tom Obsessive
Puzzles: 1293
Best Total: 20m 57s | Posted - 2006.07.25 19:18:54
Quote: Originally Posted by acorn I don't get it? Can someone explain why a single "x" near a three means anything? I can't even figure out how you got these lines in near the threes. This Friday puzzle almost killed me. |
What happens if you have this? (I really hope you do know)
You do this
Now what they were saying was that if you solved the effects of that x then you would come to a contradiction. So you end up putting a line there instead. Get it now? |
Acorn
Kwon-Tom Obsessive
Puzzles: 555
Best Total: 42m 58s | Posted - 2006.07.25 22:04:51
I guess I'll have to check it out. I've never noticed that an "x" near a three proved much of anything. But obviously it does so I'll give it a go in the next few days. Thanks. |
tilps
Kwon-Tom Obsessive
Puzzles: 6510
Best Total: 20m 22s | Posted - 2006.07.25 23:05:34
X on 3, line on 1 - both completely define a cell, so make good trial concepts because they are more likely to make some progress. X on 3 is marginally better, because you get upto 4 additional crosses as well as the 3 edges. Obtaining a contradiction sets the opposite of what you started with.
Two consecutive edges set to lines on a 3, or two crosses on a 1 are also usually reasonable, as they give anti-locked edges which sometimes can be used to propigate further. And when you obtain a contradiction, you actually make progress from a single trial, the opposite two edges of your trial get set the way you tried to set the original two edges. Two opposing edges provides the same progress, but is usually better off done using setting a single edge as above.
2's are most evil, they can make good trial points, but with much more dependence on their surroundings as to what to try. And can potentially require upto 3 trials to rule something out if there is not enough environmental restriction. A 2 with locked edges is a good trial point, it only requires a single contradiction to make progress.
Last edited by tilps - 2006.07.25 23:06:43 |
Acorn
Kwon-Tom Obsessive
Puzzles: 555
Best Total: 42m 58s | Posted - 2006.07.26 14:18:29
Thanks. I thought that the x near a three was a pattern. But it is actually just a point to try from. I usually use 3s and 1s when I am stuck. From reading other posts I get the impression that a lot of people can see fairly far ahead where a loop will end. Must have been all the partying I did in my younger days because I can only see a few steps ahead and have to use fix position to see what is going to happen. |
