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Domino & Grid Rules

Thinking Skills · Y4 OC
Year 4 OC
Lesson Guide
Explanation
Grid-rule puzzles hand you a placement law — a typical one: a new domino may not place a number so that it touches a matching number on a neighbouring tile — and ask what can or can't be placed. The game isn't dominoes; it's applying a neighbour rule EXACTLY. Two precision points: 'next to' means sharing an edge (diagonal contact usually doesn't count), and the rule applies to every touching pair, not just one side. Each check is local: pick a gap, list the numbers its edges touch, apply the rule. No cleverness — just complete checking.
Your Turn
Rule: no same numbers touching. A gap's neighbours are 2 (above) and 6 (left). Can a 2|4 tile go with the 4 facing left? Check: 2 sits by the 6 side? Place it: 2 touches above-2 → depends which half touches which edge. If the 2-half touches the 2 — forbidden.
Watch Out
A domino has TWO halves — check what EACH half touches. Half the errors come from checking only one end.
Explanation
The winning routine is the GAP AUDIT: before touching the options, go to each empty square and list the numbers its edges touch. A gap touching 2, 4 and 5 may not hold 2, 4 or 5 — its allowed set is {1, 3, 6}. Do this for both squares a domino would fill and you get two allowed-sets; a candidate domino fits only if its halves match the sets in some orientation. Auditing first turns each option check into a two-second lookup instead of a fresh puzzle.
Your Turn
A gap touches 1, 3 and 6. Which numbers can it hold (of 1-6)? Check: 2, 4, 5.
Watch Out
Audit ALL touching edges — gaps in corners of the layout often touch three numbers, not two. Miss one and the audit lies.
Explanation
A typical question offers five spare dominoes and four PAIRS, asking which pair can NOT complete the square. Read the direction of the question carefully: 'cannot' means EVERY arrangement fails — each domino in either gap, in either orientation. That's up to eight tiny checks per pair, but the gap audit makes each one instant. Strategy: for three of the pairs a working arrangement usually jumps out quickly — verify and move on. Spend your care on the suspicious pair, exhausting all its arrangements before declaring it the answer.
Your Turn
Gap 1 allows {1, 3}; gap 2 allows {2, 6}. Pair offered: 1|2 and 3|6. Can it work with one domino per gap? Check: no domino fits a single gap here — but if each gap takes ONE half (dominoes lie across both), 1|2 can lie with 1 in gap 1 and 2 in gap 2 ✓, leaving 3|6 unused. Systematic trying, half by half, is the skill.
Watch Out
'Which CANNOT' flips the logic of 'which can'. Answer the question asked — the most common error is reporting a working pair.
Explanation
The other classic grid rule: every row and column holds each symbol ONCE (mini-sudoku with letters or shapes). Attack the line that's most full: a row already holding D, B and A forces its gap to C. Then CONFIRM with the crossing column — the forced symbol must be legal there too. Row proposes, column confirms. When no line is full enough to force a symbol, find the line one-short and try each missing symbol against its crossing line. OC grids are small (3×3 or 4×4) — one forced cell usually unlocks the rest in a chain.
Your Turn
A 3×3 grid uses X, Y, Z per row and column. Row 2 holds Z and X. What fills its gap? Check: Y — then verify Y isn't already in that column.
Watch Out
Both rules bind at once. A symbol forced by its row but repeated in its column means you've mis-read a cell — re-check before continuing.
Explanation
The grid toolkit: read the rule twice — it IS the puzzle, and 'next to' means sharing an edge; audit every gap before reading options; remember 'cannot complete' demands ALL arrangements fail (be exhaustive on the suspect, quick where a fit is obvious); and in row-column grids, let the fullest row propose and its column confirm. These puzzles reward method over brilliance — the child who audits beats the child who stares. Quiz and exercises!
Your Turn
Capstone: rule 'no same numbers touching'. A gap touches 1, 2, 5, 6. Which numbers (1-6) can it hold? Check: 3 or 4 only.
Watch Out
When stuck, re-read the RULE, not the grid — misremembered rules ('no same numbers in a row?') quietly replace the real one mid-puzzle.
📌 Key Points — this lesson in a nutshell
  • The rule is the puzzle: read it twice. 'Next to' means sharing an edge — diagonals usually don't count.
  • Gap audit: list what every empty square touches BEFORE reading the options; forbidden numbers fall straight out.
  • A domino has two halves — check what EACH half touches, in both orientations.
  • 'Cannot complete' means every arrangement fails: both gaps, both orientations, both assignments.
  • Row-column grids: the fullest line forces a symbol; the crossing line confirms it. Chain from there.
  • Methodical beats brilliant — audit, check, chain.
Step 1: Introduction
Step 1 of 5
A rule about neighbours The rule: a new domino may not put a number touching a matching number on a neighbouring tile. 3 | 5 2 | 4 ✓ 3 | 5 5 | 1 ✗ 5 touches 2 — different, allowed 5 touches 5 — forbidden! These puzzles are not about dominoes — they are about applying a NEIGHBOUR RULE exactly. Read the rule twice; it is the whole game. "Next to" = sharing an edge — diagonal touching usually does not count. Every check is local: one gap, its touching numbers, the rule. Repeat.
List what each gap touches 6 2 ? 4 5 Gap audit for the ? square: touches 2 (left), 4 (right), 5 (below) → the ? square may NOT be 2, 4 or 5 Allowed here: 1, 3 or 6. Audit every gap BEFORE looking at the answer options.
Which combination will NOT complete the square? Five spare dominoes (1-5), two gaps in the square, each domino usable once. Four combinations offered — three CAN complete it, one CANNOT. Find the failure. Method: audit the two gaps first. Then for each offered pair, try: domino X in gap 1 + domino Y in gap 2 (both orientations), then swap: Y in gap 1 + X in gap 2 (both orientations). If EVERY arrangement breaks the rule somewhere → that pair fails. "Will NOT complete" needs ALL ways to fail — one working arrangement rescues a pair. Be exhaustive on the pair you suspect, quick on pairs where a fit jumps out.
Every row, every column, once each A B C D C D A B D ? B A The ? row already has D, B, A → the row rule forces C. Column check: its column holds B, D so far — C is legal there too ✓ Row rule proposes; column rule confirms. Always run both.
Rule-keeper mastery 🁢 Read the rule twice the rule IS the puzzle; "next to" = shares an edge Gap audit first list what every gap touches before options Exhaust the suspect "cannot" means ALL arrangements fail Row proposes, column confirms most-full line first; chain the forced cells Grid puzzles reward the methodical, not the brilliant — audit, check, chain. Quiz and exercises!
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