GridWits
Expert tier Technique 24 of 31 Used by Smart Hint

Long Dead End

Follow a candidate through at least eight forced continuations. If the chain eventually leaves the line with no exit, the original candidate is ruled out.

How it works

  1. 1Suppose the highlighted edge is a line. Unlike a short Dead End, nothing immediately breaks, so trace each forced continuation using only the clue-count and dot rules.
  2. 2The supposition pushes the line through fourteen forced consequences across the board; at every stop there is only one legal continuation or a completed clue crosses off the alternatives.
  3. 3At the far end, that chain reaches a dot with one line and no undecided edge left to carry it onward. A Slitherlink loop cannot stop there.
  4. 4The failure travels all the way back to the original supposition, so cross off the first highlighted edge. Because this proof takes at least eight continuations to see, the grader treats it as Expert rather than an ordinary Hard Dead End.
1 0 2 3 1 2 2 2 2 1 3 2
  • Edge on the loop
  • Edge ruled out
  • Cells that establish the pattern
Next in the ladder Crossing Parity →

The loop is closed, so any straight line drawn across the whole board crosses it an even number of times. When every crossing edge in a row or column is decided but one, that last edge is forced — whatever makes the count even.