A Tiebreaker Method for Difficult Fleetoku Boards

Queens-style logic puzzles often become hardest when the board has been reduced to two plausible cells in several regions. At that point, scanning the whole grid repeatedly can feel productive without actually producing a deduction. A better approach is to isolate one unresolved pair, trace what each option would block, and compare the consequences.

You can practise this method on fleetoku, a browser-based Queens-style puzzle with 210 levels ranging from 5×5 to 11×11. It requires no download or account, so the same board can be used for a short, focused deduction exercise.

Start with the most constrained pair

Do not begin with an arbitrary region. Look for a row, column, or coloured region that has exactly two remaining candidate cells. Prefer a pair whose cells touch several other unresolved regions, because resolving it is more likely to create a chain reaction.

Label the two cells A and B on paper or mentally. The purpose is not to guess between them. It is to ask what the board would look like if A were occupied and then repeat the same check for B.

Trace three kinds of blocking

For each candidate, mark the cells it would eliminate through the puzzle's placement rules:

1. Cells in the same row.
2. Cells in the same column.
3. Cells that conflict through adjacency restrictions.

Now inspect every affected region. If choosing A would remove all candidates from another region, A is impossible and B must be used. If both options remain possible, compare whether one option forces another region down to a single cell. That forced follow-up may be the deduction the original scan missed.

Keep deductions separate from assumptions

When testing a branch, use temporary marks rather than permanent placements. A dot can represent a cell still allowed by confirmed information, a small cross can mark a confirmed elimination, and a question mark can show an elimination that exists only inside the temporary A-or-B test.

This separation prevents an assumption from leaking into the main board. If a branch produces no contradiction, erase only the question marks and test the other candidate from the same confirmed state.

Compare regions, not individual cells

The strongest consequence is often visible at the region level. Suppose candidate A blocks two cells in a neighbouring region, leaving that region with one option. That forced option may then clear an entire row and resolve a third region. Candidate B might not create an immediate contradiction, but A creates a useful sequence of forced moves.

Follow each branch only until it either fails or reaches a stable board. There is no need to solve the whole puzzle hypothetically. The goal is to find the first definite difference between the two branches.

Use board size to control the depth

On a 5×5 or 6×6 board, a short two-step consequence check is usually enough. Larger boards can contain several overlapping pairs, so work locally and stop after three forced consequences. If neither branch produces a contradiction within that depth, move to a different constrained pair rather than extending a speculative chain.

This limit keeps the method logical and repeatable. It also makes mistakes easier to audit, because every temporary conclusion can be traced back to a single A-or-B choice.

A compact routine

1. Find a row, column, or region with two candidates.
2. Test candidate A with temporary marks.
3. Stop immediately if another region loses its final candidate.
4. Record any forced single that follows.
5. Reset to the confirmed board and test candidate B.
6. Keep only consequences proved by contradiction or by an unavoidable single.

The routine replaces broad rescanning with a controlled comparison. Difficult boards become easier to reason about because every move has a visible cause, and temporary assumptions never become accidental facts.