7
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Can you solve this Slitherlink puzzle that I came up with?

enter image description here

And in CSV:

3 - 3 - 2 -
- 2 - 2 - 2
- - 1 1 2 2
1 - - 2 - 2
2 - - - 2 -
1 2 - - 1 -

I tried to incorporate a trick or 2 that I haven't seen elsewhere on slitherlink pattern sites. That doesn't necessarily mean you can't solve it another way, of course.

First time posting here, so any feedback (positive or negative) would be appreciated

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  • $\begingroup$ Which trick did you use. I managed to solve it with what I already knew. $\endgroup$ – Kruga Oct 6 '17 at 8:00
  • $\begingroup$ @Kruga instead of doing what Wen1now did with the 2 he circled, I looked at the square to the South-west of it. Because lines go into the square on opposite corners, we know that square is a 2. This lets us chain the NW line coming in to the SE, getting the 1. You can do something similar to the corner. $\endgroup$ – MildlyMilquetoast Oct 6 '17 at 8:08
  • $\begingroup$ Also, chaining 2s also works with corners, so if a 2 doesn’t have a connection on a diagonal it transfers that state to other connected 2s on that diagonal, much like it does if there were connections. This lets us branch off of that diagonal because not having a connection in one diagonal means there is one on the other. $\endgroup$ – MildlyMilquetoast Oct 6 '17 at 8:13
  • $\begingroup$ To solve that part, I used the fact that any region has an even number of lines entering it. And I knew exactly 1 line had to enter through the chained 2, so there had to be a line below the 1. It's funny that we solved that part in 3 different ways. $\endgroup$ – Kruga Oct 6 '17 at 8:27
  • 1
    $\begingroup$ This was a lot of fun to solve! Welcome to the site proper - I hope to see more from you! c: $\endgroup$ – Deusovi Oct 6 '17 at 8:31
5
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The answer is

Yes, I can

Proof:

enter image description here

(This was very well done, although it's a shame that the methods I used were taught to me by my Slitherlink Master - i.e, they were not new to me)

Method of solution:

Firstly,

Do the obvious 3 in the top left. Now use two chains (we will use these a lot) to deduce the crosses:
enter image description here
I'll give a link to a wiki explanation for two chains

Next,

Bounce the chain back the up-right diagonal to get this:
enter image description here

Now, fill in some obvious stuff and do another chain, one below this one (a blend of twos chained diagonally, with 0 entrances on one end - if we have this:

 x
x2
  2
   2

then there must be exactly one entrance and exit to the top right and bottom left of each two)

Doing this and using a two chain gives this:

enter image description here

After which we can do another two chain, North West from here:

enter image description here

Do some basic deductions now, and finish the bottom left corner:

enter image description here

Now more basics:

enter image description here

Two chain from the top right line south west to get an additional line

enter image description here

Two chain to get an additional link:

enter image description here

The circled two has two choices (diagonal chained twos), and the right-bottom choice is ruled out since it would kill the one. So we can deduce a bunch:

enter image description here

The end is easily obtained, after crossing out the other one:

enter image description here

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  • $\begingroup$ Can you prove it's unique, though? $\endgroup$ – boboquack Oct 6 '17 at 7:53
  • $\begingroup$ Yep, was editing in now. By philosophy for grid-deductions is answer first, then edit in an explanation later. $\endgroup$ – Wen1now Oct 6 '17 at 7:59
  • $\begingroup$ I solved it my way. I've only heard of some basics like 3 next to 0, but worked out many strategies solving many slitherlinks. Started with 3 like you. Then followed in diagonal: exactly one of the two edges of 3 (bottom and right) is on, so exactly one of the two edges of 2 (TL) is on, so exactly one of 2 (BR) so exactly one of 1 (TL), so 1 buttom and right are both off. The 2 following has therefore both or none UL and both or non BR, so exactly one of TR. Go diagonaly up right like earlier with exactly one of two edges on... I guess that's what you call "two chains", don't know "bouncing". $\endgroup$ – Heimdall Aug 29 '18 at 8:23
  • $\begingroup$ @boboquack I solve this sort of puzzles (slitherlink, (killer) sudoku, kakuro, hashi, ...) with deduction. I don't just try to find a solution that fits, I look for certainties (once you eliminate all but one possibility, the remaining one must be right). The sets of possibilities can vary: number 3 has 4 possibilities (which edge is off). A loose end has 3 possibilities (straight on, turn left or turn right). 2 in a corner has 2 possibilities (the two corner edges or the other two edges). A single edge has two possibilities (on/off). Eliminating a possibility can take a lot of working out. $\endgroup$ – Heimdall Aug 29 '18 at 8:30
  • $\begingroup$ But sometimes it's important which set of possibilities involving the same edge you choose as one set can keep you scratching your head whilie the other set helps you work it out easily. But all I do is logical deductions. So everything filled in (eventually the whole solution) is logical consequence of the given puzzle. In other words, the solution I get has to be the only one. Another way to explain it is: f there are at least two possible solutions, you can't make a deduction about where they differ, you can't eliminate all cases but one because at least two cases are actually possible. $\endgroup$ – Heimdall Aug 29 '18 at 8:41

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