Aligned Triple Exclusion Sudoku: Three Cells, One Verdict

From aligned pairs to aligned triple exclusion sudoku

Aligned pair exclusion studies two cells that see a common region and asks which pairs of values they could legally take together. Aligned triple exclusion sudoku does the same for three cells that are mutually aligned, meaning each pair of them shares a house, so no two may repeat a value. You list every combination the three cells could adopt, then throw out the ones that break a rule. Any candidate that survives in no legal combination is impossible and can be erased. The power comes from checking three cells together, which catches contradictions that no single cell reveals on its own, and it is a natural graduation for solvers who already trust aligned pairs.

The role of an almost locked set

The engine behind the exclusion is usually an almost locked set, a group of N cells that together show only N plus one candidates. Such a set is one value away from being fully locked, so it can spare exactly one of the values the aligned cells might want. If a candidate combination for the three aligned cells would steal two of the set values, the set would have too few candidates left to fill its own cells, which is illegal. That combination is dead. Working through the combinations, you often find that one specific candidate in one of the three cells cannot appear in any survivor, and that candidate is your elimination.

A compact worked example

Place three aligned cells in column c4 inside box 5: r4c4 reads 5, 6 and 7, r5c4 reads 6 and 7, and r6c4 reads 5 and 7. Because they share the column, no value may repeat among them. Now suppose these three all see an almost locked set in box 5 made of two cells showing 5, 6 and 7. That set must keep at least two of those three values for itself. Test the trios: any assignment that hands both 5 and 6 to the aligned cells strips the set below survival, so it is banned. Grind through the legal trios and the 7 in r4c4 never survives, because keeping 7 there forces the banned split. You erase 7 from r4c4.

1. Find three cells that pairwise share a house, so none may repeat a value.
2. Confirm the three cells all see the same nearby almost locked set.
3. List the candidate trios the three cells could take together.
4. Delete any trio that leaves the almost locked set without enough candidates.
5. Erase any candidate that appears in no surviving trio.

Why Shapedoku makes it manageable

Aligned triple exclusion sudoku is demanding because it asks you to hold several candidate lists at once, and tidy notes are essential. Shapedoku shows candidates as small shapes, and Notes with smart cleanup removes ones that can no longer be true, which shrinks the number of trios you must test by hand. When you want to check your reasoning, the free solver on shapedoku.com can confirm the exclusion and point to the almost locked set that powered it. If you enjoy this kind of careful sorting, Astro Jam from the studio SnailPixel is a lighter match-and-clear puzzle for between sessions, and Extreme mode at app.shapedoku.com is where triple exclusion truly earns its keep.