Bowman's Bingo (Nishio)

Expert

Last-resort systematic trial and error; a candidate is assumed and all consequences traced until solution or contradiction.

How It Works

The last resort when all other techniques fail. A candidate is placed in a cell and all consequences are traced. If a contradiction arises, the candidate is eliminated; if a solution is reached, the value is confirmed.

Purists avoid this technique, but it can solve any puzzle. Essentially an intelligent brute-force search.

Example

3	489	1	2	45689	4589	58	7	68
2	5	678	467	4678	478	1	3	9
7	789	6789	15679	1356789	135789	258	4	268
1	2	37	467	34678	3478	78	9	5
8	37	5	179	1379	1379	6	2	4
9	6	4	57	2578	2578	3	1	78
47	14789	789	1479	12479	6	27	5	3
5	1347	37	8	1247	1247	9	6	27
6	79	2	3	579	579	4	8	1

Key cells of the techniqueCells where elimination is appliedCandidate to be placedEliminated candidate (crossed out)

Practice with a Real Puzzle

This 9×9 puzzle is solver-verified to require this technique on its solution path.

Expert25 givens