ALLSOLVEONETHE LIVE LOGIC PUZZLE
LATIN-SQUARE LOGIC

The structure underneath every AllSolveOne puzzle.

Learn the Latin-square rule behind AllSolveOne: why each 6x6 row and column contains 1–6 once and how that structure combines with cage sums.

At the heart of AllSolveOne is a 6×6 Latin-square rule: every row and every column contains each symbol—in this case the digits 1 through 6—exactly once.

Why the Latin rule is powerful

It creates two independent uniqueness constraints for every cell. A digit that is legal in a cage can still be eliminated because it already appears in the same row or column.

How cages change the classic structure

A plain Latin-square puzzle is mostly about placement. Cage sums add arithmetic groups that cross the row and column structure, creating additional relationships between cells.

How the Chain preserves structure

When AllSolveOne generates the next solution, exactly six positions retain their previous values and the other thirty positions are forced to change. Those six carried positions are selected one per row and one per column.

Put the idea into practice

The fastest way to understand the interaction between row, column and cage constraints is to solve a board. Start with the free practice puzzle, then enter the live world when you are ready to race for Discoverer.

Explore real completed puzzlesThe AllSolveOne Puzzle Archive contains actual Chain Puzzles with their boards, difficulty profiles, Discoverers and solve statistics.
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