Grouped Nodes Sudoku: Using a Cell Cluster as One Chain Link

What grouped nodes sudoku chains add

A chain in Sudoku links candidates with strong and weak connections. A strong link says at least one of two spots must hold the value; a weak link says at most one of them can. Grouped nodes sudoku chains widen this by letting a whole group stand in for a single candidate. When a value inside a box is confined to two or three cells that all share one row or one column, that little group behaves as one node. If the value is true anywhere in the group, the node is on, and the chain continues from there just as it would from a lone cell. That extra reach is what turns a stalled position into a solved one.

How a group forms a link

Consider the digit 3. In box 3, which spans rows 1 to 3 and columns 7 to 9, suppose 3 can only go in r1c7 and r1c8. Those two cells share row 1 and are the only homes for 3 in their box, so together they form a strong node: box 3 must place its 3 somewhere in that pair. The group also reaches out along row 1, because any 3 elsewhere in the row cannot coexist with it. That outward reach is a weak link to the rest of the row, and it is exactly what a chain needs to travel onward. The key habit is to weak-link only to cells that see every member of the group.

A worked grouped deduction

Stay with that group of 3s at r1c7 and r1c8. Since box 3 forces a 3 into row 1 through the group, no other cell in row 1 may hold a 3. If r1c2 currently lists 3 as a candidate, it must lose it, because row 1 already spends its 3 inside the group. Now imagine column c2 has 3 only at r1c2 and r5c2. Removing 3 from r1c2 leaves r5c2 as the sole home for 3 in that column, so r5c2 is solved as 3. The group acted as one node from start to finish, carrying the logic from box 3 into a placement three rows away.

• Scan each box for a digit pinned to two or three cells.
• Check whether those cells all share one row or one column.
• Treat that aligned cluster as a single node when you build a chain.
• Send a weak link out along the shared line to the next candidate.
• Follow the chain until it forces a placement or an elimination.

Grouped nodes in Shapedoku

Grouped nodes reward a board you can read at a glance, and Shapedoku helps by drawing each value as a distinct glowing shape. A group of the same shape locked to one row inside a box stands out clearly, which makes the node easy to trust. Notes with smart cleanup keeps the candidate groups tidy so you are not fooled by leftovers that should be gone. When a chain gets long, the free solver on shapedoku.com can replay it and show where the grouped node did its work, and if you want to understand a move, the first Hint is free and describes why a shape fits. Extreme mode at app.shapedoku.com is full of positions where a grouped node is the only way forward.