Almost Locked Candidates Sudoku: Intersections That Eliminate

From locked to almost locked

Start with ordinary locked candidates, the move you already use. When a digit inside a box can only go in cells that also lie on a single row or column, it is pointing, and you may remove that digit from the rest of that line outside the box. The reverse, claiming, works when a digit on a line is confined to a single box, letting you clear it from the rest of the box. Almost locked candidates sudoku builds directly on this by studying the small intersection where a box and a line cross, the two or three cells they both share.

The word almost is the whole trick. Instead of a digit being fully locked to that intersection, it is locked there except for one escape cell just outside it. That single near miss, when it meets a second near miss, is what produces brand new eliminations that plain locked candidates cannot find on their own.

How almost locked candidates sudoku combines two sets

Picture two digits, each almost confined to the same box line region, and each with exactly one cell of escape. If those escape cells interact so that only one arrangement of the two digits avoids a clash, then any candidate that would force the impossible arrangement can be eliminated. In formal terms this is the locked candidate cousin of almost locked set logic, working on a compact intersection rather than across two whole houses, which is what keeps it tractable to spot by eye.

• Look at the two or three cells where a box and a line overlap.
• Find a digit that is locked to that region except for one outside cell.
• Pair it with a second digit sitting in a similar almost locked state.
• Eliminate any candidate that clashes with every legal combination of the two.

A worked example on an intersection

Take the intersection of box 1 and row 3, the cells r3c1, r3c2 and r3c3. Suppose the digit 4 can only appear in box 1 at r3c1, r3c2 or the escape cell r1c1, and the digit 7 can only appear in box 1 at r3c2, r3c3 or the escape cell r2c3. Both digits lean heavily on row 3 inside the box. If you can show that placing 4 at its escape r1c1 and 7 at its escape r2c3 would leave some other cell in box 1 with no candidate at all, then that double escape is illegal, which forces at least one of the two digits back onto row 3. From there, a cell in row 3 outside box 1 that still lists both 4 and 7 can often be trimmed, because those digits are being pinned into the intersection. The exact eliminations depend on the grid, but the shape of the reasoning is always this: two near locked digits competing for the same few cells leave certain outside candidates with nowhere to live.

Why the eliminations are reliable

Like plain pointing and claiming, almost locked candidates sudoku rests on counting, not on assuming the puzzle has a unique solution. Each intersection can hold only so many digits, and once two near locked digits are competing for the same small set of cells, some outside candidates simply cannot survive. That makes the method completely safe on any grid, including the ones where you deliberately avoid uniqueness based shortcuts. The eliminations are often modest, one or two candidates, but they tend to arrive at the exact moment when nothing else on the board will move, which is when they are worth the most.

Telling it apart from pointing and claiming

It helps to keep the family straight. Pointing and claiming each rely on a single digit being fully locked to a row, column or box. Almost locked candidates sudoku is a step up, because it deliberately allows one escape per digit and then uses the interaction between two such digits to close the gap. If you find yourself thinking this digit would be locked if only that one annoying cell were not in the way, you are already looking at the setup for the move. The next question is always whether a second digit shares the same intersection with its own single escape.

Getting the feel in Shapedoku

Intersections are easy to picture in Shapedoku, where every digit is a bold glowing shape and the two or three overlap cells stand out clearly against the dark board. To practice almost locked candidates sudoku, keep pencil Notes on, focus on one box line crossing at a time, and ask which shapes are nearly stuck inside it. Smart Notes Cleanup keeps the picture tidy as you test ideas, so you are never misled by a stale mark. Work these on Hard and Extreme puzzles, where box line tension is common, and once pointing and claiming feel automatic, this is the natural next rung of the ladder to climb.