Futoshiki boards look clean enough that many players refuse notes until Medium or Hard humbles them. Pencil marks (candidate digits) are the cheapest way to hold Latin bans and inequality ranges in one place. This guide covers what to write, when to erase, and how to use marks on ProPuz even if the play UI is primarily direct entry.
What a mark means
A candidate in a cell means: “this digit is still possible given everything I currently know.” It is not a prediction and not a preference. If you cannot defend a candidate against a printed inequality or a row duplicate, it should not be written.
Full marks list every remaining possibility. Sparse marks list only contested digits. Either style works if you stay consistent within a puzzle.
Seed marks from Latin uniqueness
For each empty cell, start from {1…n} and delete digits already present in its row or column. That is the Sudoku-like half of Futoshiki marking. On 4×4 this is quick; on 7×7 it prevents silent duplicates that waste ten minutes.
Update the whole line when you place a digit: every peer cell loses that candidate. Batch the erasures immediately—stale Latin marks are poison.
Trim marks with inequalities
If A > B, then every candidate in A must exceed at least one surviving candidate in B—and more tightly, max(B) < max possible pairing. Practically: delete from A any digit that cannot beat every remaining option? Better: delete from A any digit ≤ the minimum possible in B once B’s range is known, and delete from B any digit ≥ A’s maximum.
Simple starter rule: if A > B and A’s candidates are {2,3}, B cannot be 3 or 4 on a 4×4. Apply edge-by-edge after the Latin seed. Revisit edges when either side’s set shrinks—see inequality chains for multi-edge ranges.
Singles fall out of honest marks
When a cell’s list shrinks to one digit, place it. When a digit appears in only one cell’s list inside a row, place it there (hidden single). Marks exist to make these singles obvious. If you never look for them, you are journaling without reading.
After placement, erase that digit everywhere it is now illegal and re-trim inequalities. The loop is: place → Latin wipe → inequality trim → scan for new singles.
Paper versus screen
On printables from ProPuz, write tiny candidates in corners. Keep final digits large and centered. On screen, if dedicated notes are limited, use a side notepad keyed by row-column (“R2C3: 2,3”) or mark lightly on a printed copy of the same challenge.
Do not let the interface’s simplicity talk you out of notes on Hard boards. The generator does not owe you a puzzle solvable from memory alone.
Stale marks: the #1 failure mode
Players erase poorly. A candidate killed by a new fill remains, then guides a false placement, then Check fails, then they blame Futoshiki. The fix is ruthless hygiene: every constraint change triggers candidate updates before the next creative idea.
If marks become chaotic, pause and rebuild from scratch for unfinished cells only. A two-minute rebuild beats a twenty-minute tangle.
Marks and guessing
Marks do not excuse coin flips. A cell with {2,3} is an invitation to seek a killer constraint, not to randomize. Use a short contradiction probe only when you can undo cleanly—discussed in solve without guessing.
Never add a candidate “just in case.” Inflated lists hide singles.
Lightweight marking for Easy
On Easy 4×4 you may mark only cells touched by two inequalities or only the {2,3} battles. Full grid marking is optional when mental load is low. The skill still matters: practice full marks on one Easy board per session so Medium does not feel like a new sport.
Track time-to-first-single after seeding marks. That metric trains scanning better than raw solve time.
Teaching and accessibility
For learners, color-code inequality trims versus Latin wipes once or twice so the two constraint families stay distinct. Screen-reader users may prefer a row-major candidate list spoken aloud rather than corner chicken-scratch.
Classroom sheets: leave a margin for “digits left in row” tallies—an alternative marking style that pairs well with Futoshiki’s Latin half.
A marking checklist before each fill
Before you promote a candidate to a final digit, confirm: (1) it still appears in the cell’s list, (2) it is missing from the row and column fills, (3) every inequality touching the cell still allows it, (4) no other empty cell in the line is the unique home for a different digit you are about to strand. That four-point check takes seconds and prevents “notes said so” disasters caused by half-updated lists.
After the fill, run the maintenance loop before looking for creative ideas. Creativity on top of dirty marks is how advanced-looking players still fail Easy Checks. If you use ProPuz daily challenges, keep the same checklist on every tier so Medium does not invent a second marking religion.
Optional polish: star cells whose candidate count just dropped to two. Those binary cells are where future probes or inequality finishes often happen—marking them saves search time later.
Put marks to work
Seed Latin → trim signs → harvest singles → repeat. Combine with the toolkit in beginner techniques and the pacing tips in solve faster. Generate practice on the Futoshiki hub, try a printable, and browse more guides on the articles hub.