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
- 1One sign is left in this row: the third cell is smaller than the fourth.
- 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.
- 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.
- 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.
- 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.
- 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.