Captured Candidates
If every way of making a cage's total uses some digit, that digit is in the cage — and nowhere else in its house.
How it works
- 1Take a cage that sits entirely inside one house, and list the digit sets that still make its total.
- 2If a digit appears in EVERY one of those sets, the cage must contain it wherever else the uncertainty lies.
- 3A 3-cell cage totalling 22, all of it inside one box, is {5,8,9} or {6,7,9} and nothing else. Which of the two it is stays open — but both carry a 9.
- 4Nothing cheaper reaches that. The cage rung only narrows the three cells themselves to 5, 6, 7, 8, 9 — five candidates across three cells, so no naked triple — and a hidden pair needs two digits sharing exactly two cells, where this is one digit loose across three.
- 5Yet 9 is certainly one of those three, so it is nowhere else in the box. Strike it from the other six cells.