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Strategies for Popular Number Puzzles

Bowman's Bingo

As of May 2026 this has been completely replaced with a new algorithm.

It is a property of Forcing Nets that the selection of certain candidates, whether they are ON or OFF - if the consequences are followed through - all other candidates might eventually be linked. If this is possible and there are no un-coloured ambiguous candidates AND there are no contradictions - then the whole board will have been solved in one fell swoop. Each unsolved cell will have one positive ON candidate left.

The reason this strategy is "last resort" is that finding such a candidate is very difficult and for the hardest puzzles, perhaps not present at all until more cells are solved. Also, hand tracing all the links to ensure the criteria is achieved is almost impossible for cluttered boards. For mostly solved boards you can do this but often simpler strategies are preferable.

Before May 2026 I had a very weak version of Bowman's Bingo and the page for this is here. It could occasionally find a candidate to turn off but it was never a positive assertion about the whole board. I labelled the old Bowmans 'trial an error' for being so difficult. But this new version is one hundred percent deterministic and logical. The solver will show all the links and it can be justified, so it does not cross the line in my opinion.

: Load Example or : From the Start
Let's take a look at one. This puzzle does not need Bowman's - the next strategy is a W-Wing. But I wanted to start with a puzzle board that isn't too cluttered. To follow along you will need to untick almost all the strategies before "last resort". (Note: Strong links are no longer shown beyond the start candidate).

If found, the solver will highlight the whole board as the eliminations are universal. All the pink coloured candidates are to be removed. It does not do this immediately, however. There is an "Accept?" button in the description box. Use that to remove the candidates and "take step" will show a completed puzzle.

The description also shows the start position - in this case +9[A5]. The solver checks all candidates with a positive assertion, that is it sets them ON and sees if that gives a whole board result. The solver will also put the page into edit mode "chained" and automatically hits the right candidate as if you had manually searched for it. You can try different candidates if you are curious.

I'd like to credit the work of the man behind the dxSudoku Channel for this improvement, particularly the video #103 Improved Bowman's Bingo Puzzle-Solving Technique which is a great resource for truly understanding the technique.



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Article created on 2-May-2026. Views: 422
This page was last modified on 2-May-2026.
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