# Slitherlink - It's all in the 2s

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

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

• Which trick did you use. I managed to solve it with what I already knew. Oct 6 '17 at 8:00
• @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. Oct 6 '17 at 8:08
• 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. Oct 6 '17 at 8:13
• 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. Oct 6 '17 at 8:27
• This was a lot of fun to solve! Welcome to the site proper - I hope to see more from you! c:
– Deusovi
Oct 6 '17 at 8:31

Yes, I can

Proof:

(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:

I'll give a link to a wiki explanation for two chains

Next,

Bounce the chain back the up-right diagonal to get this:

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:

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

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

Now more basics:

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