Six digits sounds small until three constraints collide in one cell. Mini Killer Sudoku on ProPuz layers cage sums on a full 6×6 Sudoku skeleton: rows, columns, and 2×3 blocks each hold 1–6 once, while cage digits sum to their labels without repeating inside the cage. Pencil marks—small candidate notes per cell—let you track what still fits before you commit. Used well, they prevent illegal cage repeats and silent block conflicts. Used poorly, they clutter the board and lie to you. This guide covers when to mark, what to mark, and how to keep notes synchronized with both cage arithmetic and unit rules.
When pencil marks earn their keep
On ProPuz Easy boards, tight cage combinations often solve the opening without notes. Marks become valuable when combination menus widen—typically Medium and above—or when multiple cages share cells and eliminations crossfire. If you complete a full scan loop from beginner techniques with zero progress, that is the right moment to note candidates rather than guess.
Another trigger: you know a cage’s legal set but not orientation. Marking {3, 5} as cage candidates in two cells preserves ambiguity until a row or block ban picks the layout. Writing a digit prematurely because “it has to be one of these” causes the duplicate-in-cage errors cataloged in common mistakes.
Unit candidates: row, column, and block
Classic Sudoku pencil marks list digits 1–6 absent from the cell’s row, column, and block. Mini Killer requires the same pass—never skip blocks because cages feel more exciting. A digit eliminated from a row must disappear from notes in every cell of that row, including cells whose cages still have budget room for that digit on arithmetic alone.
Build unit marks in batch: pick a row, scan missing digits, propagate to empty cells. Repeat per column, then per 2×3 block. On digital play, use ProPuz note mode if available; on paper, tiny corner digits work identically. Consistent placement—always lower-left for unit marks, for example—reduces visual noise on a compact 6×6 grid.
Cage candidates: sum budgets and combination menus
Unit marks alone are insufficient. A cell may allow 4 by row logic while its cage cannot host 4 without breaking the remaining sum or repeating a cage mate. After unit passes, filter each cell’s notes through cage menus from cage sums and combinations.
Practical workflow: list the cage’s legal combinations given current fills, collect every digit appearing in any surviving combination, and intersect that set with unit candidates. If 6 remains unit-legal but no combination including 6 survives, erase 6 immediately. Cage-side filtering is where Mini Killer diverges from plain Mini Sudoku—players who ignore it wonder why their neat notes still fail Check.
Erasing stale marks: the hygiene rule
A candidate killed by any rule must vanish from notes the same pass you discover the kill. Stale marks advertise false options; you combine them into sums that look plausible until ProPuz Check disagrees. The hygiene rule is absolute: one elimination, one erasure. If you cannot remember the last time you refreshed notes, run a full-board pass before continuing.
Stale marks often accumulate after cage closes. Placing the final digit in a cage changes nothing for unit marks in distant cells, but neighbors in overlapping regions may still need updates. After every cage completion, scan touching cells and reconcile notes with new sum budgets. Five boring minutes of erasing beats rebuilding half the grid from a hidden contradiction.
Cage vs unit conflicts: which wins?
Neither layer outranks the other—both are laws. When unit marks show {2, 4, 6} and cage filtering leaves {2, 4}, the cell’s true candidates are {2, 4}. When cage filtering removes everything, you have a contradiction to resolve by backing up a prior placement, not by forcing a digit anyway. Contradictions on well-posed ProPuz Easy boards usually mean a misread combination or a forgotten block duplicate, not a need to guess.
Hidden singles appear when cage and unit filtering leave one candidate. Naked pairs—two cells in a unit sharing the same two candidates—also appear once marks are honest. These patterns bridge toward advanced methods without requiring new notation systems.
How much marking is too much?
Mark empty cells only. Filled cells need no notes. On Easy, partial marking—hot regions only—is fine if the rest still yields combinations by inspection. On Hard and Expert, fuller marking prevents arithmetic slips when four cages overlap a single block. Let difficulty guide density: ProPuz tiers exist partly to train your note discipline gradually; see Easy vs Hard for tier expectations.
Avoid marking every cell on move one before reading cage labels—that reverses the correct order. Inventory tight cages first, place forced digits, then mark regions where menus remain wide. Notes support logic; they do not replace the scan loop.
Pencil marks and the no-guess philosophy
Honest notes make guessing unnecessary. If every cell’s candidates reflect both cage and unit rules, the next move is either a forced single or a deducible pattern—not a coin flip. When tempted to “try” a digit, expand marks instead; if no candidate survives anywhere, the error lies earlier in the grid. That diagnostic mindset aligns with solve without guessing.
Use Check after logical bursts, not to validate random probes. Check feedback plus clean notes teaches which layer failed: unit duplicate, broken sum, or cage repeat. Treat that feedback as a mark-update instruction, not as permission to shuffle digits blindly.
Keep your notes working for you
Pencil marks are a bookkeeping tool for a dual-constraint puzzle. Mark when menus widen, filter through cage arithmetic, erase instantly on eliminations, and never let stale candidates survive a cage close. Six digits stay readable when notes stay honest—clutter is a habit problem, not a grid-size problem.
Practice on daily challenges, revisit beginner tips, browse the article library, or open a Medium puzzle and mark one block completely before your next placement.