Conservation Questions

Each row (or each column, or both) contains the same total of each category. The per-cell counts vary freely as long as the row totals — and sometimes column totals — are invariant. The solver must deduce the missing cell's contribution to keep the invariant.

• Cells contain multi-category counts.
• The per-row sum of each category is identical across all three rows.
• The total per row is constant even though cell counts vary.

• Group-counting questions with three or more visible categories.
• Row-2 cells appear to 'rebalance' what row-0 and row-1 already supplied.
• A double-conservation question may also constrain columns.

1. 1Sum each row's total per category from the visible cells.
2. 2Confirm that the row total is identical across the visible rows.
3. 3For the missing cell, compute the row total minus the visible cells in that row.
4. 4If both rows and columns are conserved, intersect both constraints.

• Confusing conservation with addition — conservation keeps totals constant; addition grows them.
• Missing the second axis — double-conservation requires both rows AND columns.
• Nested conservation: per-row totals K_r themselves follow a meta-rule across rows.