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Sudoku Hidden Triple

Three digits' homes total three cells → erase every other candidate from those cells.

Technique 9 in the order the hint searches · difficulty Very hard · up to intersections and triples

The hidden pair with one more digit. If the cells that could take a 1, a 2 or a 6 in some unit come to only three places between them, those three cells belong to 1, 2 and 6.

In row 8, the 1, the 2 and the 6 can only go in columns 3, 5 and 8; columns 4 and 9 are shut out by the 1, 2 and 6 standing in their columns. The three digits share those three cells, so the 3 and the 9 written there come off.

Add up where three digits can go

Keep only the digits with two or three homes and try them in groups of three. If three digits' places union to exactly three cells, you have one. There are far too many combinations to work through by hand, so in practice this is one the hint finds for you.

How the hint says it

In row 5, the three digits 7, 8 and 9 can only go in r5c7, r5c8 and r5c9. Those three digits share those three cells, so the leftover candidates 3, 4 and 6 come off them.

Three digits reserve three cells

Each of 1, 2 and 6 must appear somewhere in that unit, and there are only those three cells between them. The three cells have to be filled by the trio, so any other candidate written there has nowhere to stand.

Across 300 generated puzzles it came up once. Running into one is a stroke of luck.

Puzzles that need this technique

Four puzzles with a spot where nothing moves until you use Hidden Triple. Press a number to play it.