GridWits
Expert tier Technique 10 of 11 Used by Smart Hint

Rejection Chain

Rejecting this cell would keep all of its neighbors, which rejects every copy of their numbers, which keeps more neighbors — a ripple followed as far as it forces. If it ends with a broken rule — most often two kept copies of one number in a line, or a piece of the board sealed off — the first cell can't be rejected: it's kept.

How it works

  1. 1Suppose the highlighted 3 were rejected. Rejected cells can't touch, so all four of its neighbors would be kept — including the 8 directly to its right and the 9 directly below it.
  2. 2Follow that one step further: a kept number can't repeat among kept cells, so the other 8 and the other 9 — both in the bottom row — would both have to be rejected.
  3. 3But those two sit side by side, and rejected cells can never touch. The supposition breaks.
  4. 4So the highlighted cell is kept. On harder boards the ripple runs deeper — keep following the forced marks as far as they go. Most chains end the same way: two kept copies of one number landing in a single row or column.
1 2 3 4 5 6 2 3 8 5 6 1 3 9 5 6 1 2 4 5 6 1 2 3 5 6 1 2 3 4 6 9 8 3 4 5
  • Kept
  • Cells that establish the pattern
  • Where the conclusion lands
Next in the ladder Contradiction →

Suppose the cell were rejected (or kept) and follow the consequences — if the rules break, the opposite must be true.