Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 Under the no-same-neighbours rule, can a 4 be placed next to a 4?
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No — that is exactly what the rule forbids.
2 In these puzzles, does "next to" include diagonal touching?
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No — next to means sharing an edge.
3 A row in a 4-symbol grid shows A, C, D and a gap. What fills the gap?
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B — each symbol once per row.
Level 2 · Core
4 A gap touches 1, 4 and 6. Which numbers from 1-6 are ALLOWED? (list like 2,3,5) (type)
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Banned: 1, 4, 6 → allowed 2, 3, 5.
5 A domino 2|5 goes into a gap-pair: the left square touches a 2, the right square touches a 5. Can the domino fit in SOME orientation?
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No — orientation 2|5: the 2-half sits by the 2 ✗. Flipped 5|2: the 5-half sits by the 5 ✗. Both orientations break the rule, so it cannot fit.
6 A 3×3 grid, symbols P, Q, R once per row and column. Column 1 holds P and R. What is the third cell of column 1? (letter)
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Q — the column needs one of each.
Level 3 · Challenge
7 Gap A allows {1,3,6}; gap B allows {3,4}. Domino pair: 3|4 and 1|6. Assign dominoes to gaps so all halves are legal. Which domino goes in gap B? (write it as a|b) (type)
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Gap B only allows 3 and 4 → the 3|4 domino must take B; 1|6 fits A ({1,6} ⊂ {1,3,6}) ✓
8 True or false: to prove a pair CANNOT complete the square you must check both dominoes in both gaps in both orientations.
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True — "cannot" requires every arrangement to fail; up to 8 quick checks.
9 A 4×4 letter grid (A-D once per row/column): row 3 = D, ?, B, A. Column 2 already contains C in another row. Can the ? be C?
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No — the row forces C, but the column already has one. A contradiction means a mis-read cell somewhere: re-check the grid. (Row proposes, column confirms!)