Bowman's Bingo

Bowman's Bingo is trial and error done properly. You pick one candidate, assume it is the answer, and write out every placement that assumption forces, keeping the whole trail marked so you can wipe it out again. If the trail hits a contradiction, the candidate is dead and you have gained a real deduction. If it does not, you roll back and try another.

So, do you have to guess in sudoku? Not on a well-made puzzle: it has exactly one solution, and logic can reach it. To solve a hard sudoku without guessing, work up the technique ladder first and keep Bingo for when everything you know has run out.

What the pattern is

The method has three parts, and the third is the one people skip:

• The assumption. One candidate in one cell, never two at once.
• The trail. Only forced placements: naked and hidden singles created by what you have already written. Number them so you know the order.
• The rollback. Every mark from the trail comes off the grid before you try anything else.

The trail is written differently from your real pencil marks: a second colour, a copy of the grid, or a separate list. If you cannot undo it exactly, you are not solving the puzzle any more, you are damaging it.

When to look for it

Last. After singles, locked sets, fish, wings, chains, Almost Locked Sets and forcing nets. Bingo is a legitimate deduction (a contradiction is a proof, not a guess), but it teaches you nothing about the puzzle, and it takes longer than the technique you failed to spot. Treat every use as a note to go back and study what you missed.

How to apply it, step by step

1. Update all pencil marks first. A wrong mark turns Bingo into vandalism.
2. Choose a candidate whose consequences stay forced for several steps, for example a digit with few places left in its rows and columns.
3. Assume one candidate and mark it as trail step 1.
4. Add only forced placements, numbering each one.
5. Stop at the first contradiction: a repeated digit in a unit, or a cell with no candidates left.
6. Erase the entire trail, then remove the candidate you assumed. That elimination is permanent.
7. If no contradiction appears, erase the trail anyway and pick a different starting candidate.

A worked example

This board follows only the digit 2. The trial assumes B6 = 2 and marks it as the assumption:

1. Box 2 loses its other 2s, including A4 and C5. Row A then has only A3 left for a 2.
2. In row C, C1 sees A3 through box 1 and C5 sees B6 through box 2, so C8 is the only place for a 2.
3. Row F now has nowhere to put its 2: F3 sees A3 in column 3, F6 sees B6 in column 6 and F8 sees C8 in column 8.

That is a contradiction. The trial is cleared and 2 is removed from B6. The trial places nothing on the real grid, so the result is a single elimination.

Common mistakes

• Guessing inside a guess. One assumption at a time; nested trails are unrecoverable.
• Writing placements that are merely likely. Only forced singles belong on a trail.
• Keeping the trail when it completes the grid without a contradiction. It may be a valid solution, but you have proved nothing about the other branch.
• Forgetting which marks were trail and which were real. That is how a solved puzzle turns into an unsolvable one.

Where you meet it

Bingo is the bottom rung of the ladder and belongs to whatever survives everything else: in practice, the occasional Legendary puzzle where you cannot find the pattern the setter intended. Before you reach for it, look once more for XY-Chains; most positions that seem to need Bingo are hiding a short chain in plain sight.

This page sits last on our ladder because of how you use it, not what it costs to run: trial and error is the approach a person reaches for only when every pattern has failed. Automatic raters work differently: they score by search depth and branching, so a tool like Sudoku Explainer can place some forcing-net variants above a Nishio-style contradiction chain even though both belong to the same family. Ladder position here means solving order, not a numeric difficulty score.