GridWits

Rejection Chain

Expert Used by Smart Hint

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.

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

How it works

  1. Suppose the highlighted 3 were rejected. Rejected cells can't touch, so all four of its neighbors would be kept — including the 8 above-right of it and the 9 below-left.
  2. Follow 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. But those two sit side by side, and rejected cells can never touch. The supposition breaks.
  4. So 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.