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.

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 cell with two candidates whose neighbours are also mostly bivalue.
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

r1c1 {3,8}   r1c5 {3,7}   r4c5 {2,7}   r4c1 {2,3}

try r1c1 = 3
  1. r1c5 = 7   (row 1 took the 3)
  2. r4c5 = 2   (column 5 took the 7)
  3. r4c1 = 3   (row 4 took the 2)
  -> r1c1 and r4c1 are both 3, in column 1   CONTRADICTION

erase steps 1-3, remove 3 from r1c1, so r1c1 = 8

Four cells, three forced steps, one solid elimination. It is worth noticing what really happened here: those four bivalue cells form a chain, and a solver who spotted it would have reached the same conclusion without writing anything on the grid. Bingo found it by walking instead of looking.

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.