Thinky Dailies 2-59 full logic solve
Yay, a Connectlink with a solve path that is both fully logical and comes relatively naturally! I personally didn't feel it was a 4/5 difficulty, but a lot of people on the Thinky Games Discord did (and a few claimed that they had no idea how one could logic this out), so fuck it, I will make a writeup on how the full logic solve path looks.
Let's start by marking the trivial stuff, which are the corners. Let's also cross out the spaces between the letters to make some things more clear.
Since A and R on the left can't be connected, we can safely assume there will be a corner between them and mark the appropriate line:
This allows us to mark a few critical lines in the central EMBARK cluster of letters. B can only go right, as going left would force it to connect with either A or R. This in turn forces the cluster R to go down.
With this we have enough information to resolve the bottom left corner by considering the two pairs of letters that are there – A's and R's. The line connecting the R's can go either around this corner and the EMBARK cluster, or be contained within that corner. However we can somewhat easily see that going around will prevent A's from connecting to each other.
This means that the line connecting the R's have to go inside that corner.
From this point we can resolve the pair of A's, as there is only a single way they can connect to each other. This in turn automatically resolves the pair of R's, giving us the following state.
Let's mark the forced corners...
...and the trivial lines near the cluster with the letters M and B.
Now, let's focus on the tile below the right B. It is impossible for it to be a up-left connection, as it would cause the B and K to connect to each other. This means it has to be either up-right or left-right connection. We can prove that the up-right connection is impossible, as it would block the pair of K's from connecting to each other.
To do so, let's assume that we do have that up-right connection. Then, if we draw an imaginary line between the ends of the B line, we can see it would block the letter K from connecting to pretty much anything:
The only way this arrangement could work is if the E line would go around the letter K in the top right corner – however this causes a contradiction, as it would result in a connection between letters E and B.
This leaves us with only one possibility below that letter B – so let's mark it.
We get more forced lines:
The spot below the right letter E lets us resolve the pair of B's, simply because it is forced to be a left-right connection. Any other connection would either result in E connecting with B, or a line crossing.
We get even more forced lines:
Let's now focus on the letters M and E. If we connect the current ends of the E line with an imaginary line, we will notice that it would block M's from connecting to each other. For this reason we can deduce that the E line will go around the top right M – which lets us place this line...
...and collapse the puzzle into a solution, as at this point all the remaining lines are forced.
