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Chain reasoning

Both branches of a two-way cell agree somewhere else.

Technique 7 of 7 · Updated 12 October 2026

What is chain reasoning in Binairo?

Pick a cell you can't decide. Try owl; try fox. If some other cell ends up the same either way, that other cell is settled. This is the last tool in the box and the only one that looks at the whole board. Only Tier 5 and 6 puzzles may need it, and no Hoot & Fox puzzle ever needs more than it.

Pip: Nothing cheaper works on this board. Take row 1, column 1 and try both animals. As a fox, column 1 starts with two foxes, so row 3, column 1 must be an owl. As an owl, the forced moves run right round the board — and row 3, column 1 is an owl again. Both branches agree, so place that owl, and the rest falls.

Interactive example · 1 of 1 · tap the empty cells

How to spot it fast

Save it for when nothing else works. Choose a cell where both animals look possible and where either choice sets off lots of forced moves, then compare the two outcomes.

Common mistake

Keeping the result of one branch. Chain reasoning only places cells that come out the same in both branches; anything else would be a guess.

Practise it

Unlimited puzzles let you drill any size. Other techniques: Pair → bookends · Gap fill · Count exhausted · Count pressure · Triple look-ahead · Links = and × · hard puzzles.

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