At the heart of PUZRU 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 PUZRU 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 in the 200-puzzle progressive Training Room, then enter the live world whenever you are ready to race for Discoverer.