BUG stands for bivalue universal grave: a grid state in which every unsolved cell holds exactly two candidates and every remaining digit has exactly two places left in each row, column, and box it is missing from. Such a grid can never have a unique solution — its candidates pair off into loops that can be flipped wholesale, turning any one solution into a second. Like the unique rectangle, this is a uniqueness argument: a proper puzzle can never arrive there.
BUG+1 is the position one step short of the grave: every unsolved cell is bivalue except a single cell holding three candidates. One of those three digits is the extra — the one that appears three times, not twice, in the cell’s row, column, and box.
If the cell took either of its other two digits, the extra candidate would vanish everywhere it counts and the grid would collapse into a perfect BUG — two solutions, contradiction. So the cell must take the extra digit, and it is placed outright. Spotting it is the easy part: late in a tight puzzle, when the pencil marks have thinned to pairs everywhere, look for the lone cell still showing three.
On the board
On this board every unsolved cell shows exactly two candidates — except R8C1, with {2,5,8}. Count that cell’s digits in its houses: in row 8, in column 1, and in the bottom-left box, the 2 appears three times among the pencil marks, while the 5 and the 8 each appear exactly twice. Strip the 2 from R8C1 and the whole grid becomes a bivalue graveyard with two interchangeable endings. So the 2 is not merely kept — it is placed: R8C1 is 2.
This is the exact board the app's interactive BUG+1 demo uses — step 35 of its 53-step walkthrough, drawn here with its live pencil marks.
