How to Solve Consecutive Sudoku on Paper with a Pen

Consecutive Sudoku is the puzzle where the things that are not printed matter almost as much as the things that are. Between pairs of adjacent cells sit either nothing, or a small white dot meaning "these two digits differ by exactly one." On a screen, the dots are tidy and the empty edges are easy to ignore. On paper with a pen, the empty edges are where the entire discipline lives.

What makes the variant special for paper solvers is that its strongest logic is negative: most deductions come from edges that are not marked. The no-undo rule compounds this — the moment you assume a dot where none exists, your consecutive snake silently breaks the puzzle. The workflow below, folded out of the shared pen-and-paper Series Hub, converts the whole dot network into something you can read like a subway map before you place a single 9.

The two-pen rule: finals in blue, logic noise in red. Dots are red dots, candidate bans are red strikes, and a resolved k of an i–k chain is blue the instant every other option has a strike beside it.

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1. The Rules, Stated Precisely for Paper

• Classic Sudoku holds: every row, column, and 3x3 box contains digits 1–9 exactly once.
• A white dot on the border between two adjacent cells means their digits are consecutive — they differ by exactly 1.
• An edge with no dot means the two digits must not be consecutive — they differ by at least 2. This negative statement is the skeletal rule of the whole variant.
• Dots describe neighbouring cells in all four directions: up, down, left, right. Diagonal neighbours are unaffected.
• Every puzzle has exactly one solution, and every marked and unmarked edge must be honoured in it.

The four strongest pairs to internalise: 5's only consecutive partners are 4 and 6; 1's only partner is 2; 9's only partner is 8; and once one partner of a pair is fixed, the other loses all freedom. Every chain in the puzzle is a walk along these pairings.

2. Paper Adaptation — Trace the Dot Graph in Red

Printed dots are tiny, greyish discs that vanish when the page is under a desk lamp. Rebuild them at puzzle scale before anything else:

Next, deprioritise the noise. Where the classic solver scans for candidates, the Consecutive solver scans for chains: find every cell carrying two or more dots, because those are the connective tissue your pairs and triples will hang from. Mark each chain's endpoints before you commit any digits.

3. Pass 1 — The 5-Anchor and the 1/9 End Pairs

Consecutive chains bow to three anchor rules, and all three are instant-wins on paper:

4. Pass 2 — Pair-Locking in Boxes and the Missing-Dot Ban

Now merge the dot graph with the classic house logic. A dotted pair inside one 3x3 box whose two cells share exactly two candidates — say {6, 7} — locks both digits into those two cells, so strike 6 and 7 from the box's other seven cells. That is pair-locking, and the interaction is older and forged on the naked pairs strategy page.

Run this reading on every unmarked edge you suspect: any two candidates differing by exactly 1 on an unmarked edge are mutually exclusive. This single habit — enforced in red strike ink — quietly removes the most subtle wrong moves in the entire variant.

5. Pass 3 — Candidate Merges and Endgame

Late in the solve, a cell's candidates are the intersection of three classic sets — row, column, box — with one extra filter: every dotted neighbour's partner set. Write the candidates in corner notation, then strike anything a dot forbids. When a cell collapses to a single survivor, commit it in blue and immediately re-run the neighbour-round: its dotted partner loses all freedom, and its unmarked neighbours lose a candidate one step away.

Do not hoard the audits for the finish. Woven single placements — a 4 next to a 5, a 9 next to an 8 — should be read as two solved cells pretending to be one; whenever you place one member, strike the partner map in red on the spot. The hidden pairs page and the strategy index cover the classic endgame reductions you'll still need.

6. A Dotted Box, Read as a Graph

Three red dots wind 4–5–6 down to 7 in this box. The chain 4-5-6-7 consumes four cells; everything that touches it but is not chained is meeting the missing-dot ban.

Note the two chain computations hiding in the layout. First, the dot between 4 and 5 chains back to nothing — 4's left edge is bare, so its left neighbour must differ by at least 2, pinning that neighbour away from 3 and 5 at once. Second, the vertical dot from 6 down to 7 completes the walk 4-5-6-7; 7's bare right edge then bans its right neighbour from ever being 6 or 8, so the 8 sits diagonally clear instead. Chains do the enforcement on Consecutive grids — the classic houses just keep score.

7. The Three Moves That Break Consecutive Boards

7.1 The 5-Based Pairing (i and i+1)

Every consecutive relationship is an ordered pair (i, i+1). Fix one element and the other is wholly determined; that determinism propagates like a lockstep. A chain of three dots writes down its five possible reassignments in two minutes: 1-2-3, 2-3-4, 3-4-5, 4-5-6, 5-6-7, 6-7-8, 7-8-9. Whatever the middle cell's box already possesses strikes most rows off the list, and one survivor fixes the whole run.

7.2 The Unmarked-Adjacency Ban

The rule the variant is built on inverts naturally: a missing dot is a hard not-consecutive constraint. Whenever a candidate pair sits on a bare edge and the two digits differ by 1, exactly one of them can survive there. Strike the loser in red and let the row's naked singles do the rest — this is the fastest elimination per second of effort in the whole variant.

7.3 Dot-Aware Pair Locking

Locked pairs on Consecutive boards come in two flavours: classic naked pairs inside a house, and dot-forced pairs where a chain pushes two specific digits into two specific dotted cells. The second flavour outranks the first — a dot-forced 4/5 pair on an edge is a permanently resolved adjacency, and every reader should treat it as such. See naked pairs and hidden pairs for the house-side drill.

8. Common Paper Mistakes on Consecutive Boards

• Forgetting the missing-dot ban. The reflexive "two candidates that differ by one look nice" reflex is lethal here. Verify the edge is dotted before accepting a {k, k+1} pair.
• Treating a 5 as flexible. A dotted 5 is a 4/6 fork, not a free digit. Strike every candidate but 4 and 6 from its dotted neighbour immediately.
• Over-clamping into straight snakes. The digits along a dot chain are consecutive but never strictly ordered by position — the pair (5, 6) can sit either way around the edge. Commit an orientation only when a house forces it.
• Auditing only the dots at the end. A misplaced bare-edge breaks the puzzle invisibly. Verify as you solve: every dot = ±1, every bare edge = at least ±2.

9. Train the Chain Eye, Then Carry It to Paper

Dubbed chains are musicians, not mechanics — drill them on any grid where houses are tight. NetSudoku classic tiers are ideal rehearsal space: run Easy and Medium boards while narrating every pairwise relationship out loud, then stress-test at Hard and Expert. Pair that with the X-Wing technique guide for the fish patterns the endgame will still ask of you.

Once the dot graph feels like a subway map, the same two-colour discipline ports straight across the family — including the shaded-parity reading of Odd-Even Sudoku, where the extra constraint is a colour instead of a dot.

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Honour Every Dot the Logical Way

Turn the printed clue sheet into a validated solve — play the same board on NetSudoku with auto-notes disabled and compare the adjacency map against the generated solution.

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