Bowman's Bingo (Nishio)

Extreme

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

1	2	58	9	7	4	2	5	8
7	5	4	8	6	1	4	9	6
6	8	1	5	9	37	6	4	5
4	9	6	3	5	8	1	56	9
9	4	5	6	37	9	8	3	56
5	6	3	4	28	6	57	9	7
2	5	4	9	38	27	5	6	3
49	8	37	56	4	9	6	58	4
58	6	9	7	56	4	38	7	9

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

R5C5={3,7}. Try 3 first → Contradiction reached → R5C5≠3 → R5C5=7.

Practice with a Real Puzzle

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

Expert25 givens

1	2	58	9	7	4	2	5	8
7	5	4	8	6	1	4	9	6
6	8	1	5	9	37	6	4	5
4	9	6	3	5	8	1	56	9
9	4	5	6	37	9	8	3	56
5	6	3	4	28	6	57	9	7
2	5	4	9	38	27	5	6	3
49	8	37	56	4	9	6	58	4
58	6	9	7	56	4	38	7	9

1	2	58	9	7	4	2	5	8
7	5	4	8	6	1	4	9	6
6	8	1	5	9	37	6	4	5
4	9	6	3	5	8	1	56	9
9	4	5	6	37	9	8	3	56
5	6	3	4	28	6	57	9	7
2	5	4	9	38	27	5	6	3
49	8	37	56	4	9	6	58	4
58	6	9	7	56	4	38	7	9

1	2	58	9	7	4	2	5	8
7	5	4	8	6	1	4	9	6
6	8	1	5	9	37	6	4	5
4	9	6	3	5	8	1	56	9
9	4	5	6	37	9	8	3	56
5	6	3	4	28	6	57	9	7
2	5	4	9	38	27	5	6	3
49	8	37	56	4	9	6	58	4
58	6	9	7	56	4	38	7	9