Aligned Pair Exclusion in Sudoku Explained

Begin with two base cells and their combinations

Aligned Pair Exclusion, usually shortened to APE, begins with two unsolved base cells. In the simplest form, the cells see each other because they share a row, column, or box. Write the candidates for both cells and list the possible pairings. If the first cell contains heart or circle and the second contains circle, crescent, or lotus, combinations using circle in both cells are already impossible because peer cells cannot contain the same shape. The remaining combinations must then be tested against nearby constrained groups. APE does not try one pairing on the board and continue from it. It examines every pairing as a temporary logical case. The goal is to discover whether a particular candidate in one base cell appears only in pairings that create an immediate contradiction. If so, that candidate has no valid partner and can be removed. Full Notes are important because the list of possible pairings is only reliable when both base cells contain every legal candidate.

Use Almost Locked Sets to reject impossible pairings

The usual attacking structures are Almost Locked Sets. An Almost Locked Set contains N cells with exactly N plus one candidates between them. Two cells containing heart, crescent, and lotus form a simple example. If outside placements remove two of those three shapes from the set, the two cells would be left with only one candidate between them, which is impossible. Suppose both base cells see every cell in that set. A temporary pairing that places heart in one base cell and crescent in the other would remove both heart and crescent from the set, leaving only lotus for two cells. That pairing must be rejected. Repeat this check for every base-cell combination against every relevant Almost Locked Set. If every combination containing heart in the first base cell is rejected, heart can be removed from that cell. The final elimination comes from exhausting all legal partnerships, not from choosing one preferred branch.

Keep the search small and verify it backward

APE becomes difficult when the base cells have many candidates or when several large Almost Locked Sets are involved. Learn it with bivalue and trivalue cells near small two-cell sets. Create a compact table of pairings rather than holding them in memory. Cross out combinations that duplicate a symbol in the base unit, then cross out those that leave an attacking set with fewer candidates than cells. When one candidate disappears from every surviving row or column of the table, you have an elimination. Before applying it, verify the logic backward: confirm the base candidates, confirm that both base cells see the required candidates in the attacking set, and recount the set's cells and combined candidates. In Shapedoku, use Notes on Hard or Extreme and let smart cleanup remove only candidates affected by confirmed placements. APE is a precision technique. One clean elimination is enough; afterward, rescan for singles, pairs, and wings before building another exclusion table.

1. Choose two unsolved base cells with small candidate lists.
2. List every candidate pairing that the two cells could take.
3. Remove pairings that immediately duplicate a shape in a shared unit.
4. Find small Almost Locked Sets seen by both base cells.
5. Reject pairings that would leave any set with fewer candidates than cells.
6. Remove a base candidate only when no surviving pairing contains it.