GridWits
Hard tier Technique 13 of 20 Used by Smart Hint

Line Consistency

Every way this row or column's remaining values can be ordered while obeying the signs inside it was checked — a value eliminated here appears in none of them.

How it works

  1. 1One sign is left in this row: the third cell is smaller than the fourth.
  2. 2Read that sign on its own and it strikes nothing. The third cell tops out at 3 and the fourth starts at 2, so neither end has a candidate the other rules out.
  3. 3So enumerate instead. Of every way 1, 2, 3 and 4 could fill this row, only two survive the candidates AND the sign: 1-2-3-4 and 2-4-1-3.
  4. 4The fourth cell is 4 in one and 3 in the other, never 2 — strike it. What did the work was weighing the sign against the fact that these four cells share four values, which no single pair of cells can see.
  5. 5How much work this move is depends on how many cells are still blank — two blanks is a single pair to weigh, six is seven hundred and twenty orders. The grader charges the same either way, because it is the same move: a longer line is more bookkeeping, not a harder idea.
1 2 2 4 1 3 2 3 4 <
  • Candidates this technique rules out
  • Smaller → larger — The arrow follows the direction imposed by the inequality sign.
  • Allowed line orders — The long arrow marks the whole row or column whose orders are checked.
  • Conclusion — The coloured candidate, or the final arrow when it lands outside the pattern, shows the result.
Next in the ladder XY-Wing →

A cell with two candidates links to two other two-candidate cells that share one candidate each with it and one with each other — the shared value can't be in any cell both of those see.