3
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I got this Loopy (Cairo) puzzle, but got stuck here:

loopy puzzle #9x9t4:a14d3d42m1d3a4a3a33d43113b4233b1c1d3f121a2a33a322323a34i33a3a2c33a43a23b2a4c334b2b2d204c

I have no idea how to proceed without guessing with backtracking. Are there any local deductions possible here?

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4
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At the bottom right corner

the intersection between the 2 and 4 cannot have two edges belonging to the 4 or two edges belonging to the 2, nor can it have no edges marked. Therefore, the rest of the edges around the 4 and around the 2 can be filled in.
enter image description here
After that the string of 3s next to the 4 follow easily.

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6
  • 1
    $\begingroup$ You're right. I keep missing this kind of local patterns. =| $\endgroup$ – user21820 Nov 22 '20 at 9:30
  • $\begingroup$ After that I get to this and get stuck again. What's next? $\endgroup$ – user21820 Nov 22 '20 at 9:47
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    $\begingroup$ You really should remove the unused edges. Then you would more easily see that you can do something at the 3 just to the upper left of the 2&4 that I wrote about. $\endgroup$ – Jaap Scherphuis Nov 22 '20 at 9:57
  • $\begingroup$ I don't get it; there are still 2 possibilities for the edges around that 3. I have to check quite far (≈10 moves further) to eliminate one of them. $\endgroup$ – user21820 Nov 22 '20 at 13:30
  • $\begingroup$ @user21820 There are two possibilities for that 3, but in either case the adjacent edge pointing to the left is not used and can be removed, which in turn allows you to deduce more. $\endgroup$ – Jaap Scherphuis Nov 22 '20 at 15:08

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