Logic puzzles

Working it out with nothing left to guess. On most of these boards the arithmetic is deliberately light, so what is left is the reasoning.

Stirring Paint has no arithmetic in it at all: a colour, a direction and a jump for every cell, until each colour closes a single loop. Hitome’s Garden and Hitome’s Paddocks turn on binary choices — every line has exactly two ways to go — which is what makes them deducible rather than merely searchable. Finding Zero and Finding the Longest are about using an answer you have already paid a turn for. Gozen, Zebra and Balanced Zebra put the same reasoning inside a game, where the other side is reasoning too.

9 puzzles

• Finding the LongestThe longest road in a tree is found by walking away from anywhere twice — a guess by eye, then a count to check it. · grades 1–6
• Finding ZeroEvery number turned over says how far zero is, so the hunt closes in by reasoning rather than guessing. · grades 1–6
• Stirring PaintDeduction with no arithmetic in the way — colours, directions and jumps, worked out until every loop closes. · grades 2–6
• Hitome's GardenEvery line has just two ways to go, and the walls they make decide which flowers end up sharing a bed. · grades 2–6
• Hitome's PaddocksA sheep is worth the squares in its own field, and the two flocks have to end up worth the same. · grades 2–6
• KajitsuCutting fruit into pieces of a given size and symmetry: every morsel has to fold or spin onto itself. · grades 3–6
• Balanced ZebraBoth colours have to multiply out to the same number, and then to the largest that shape allows. · grades 3–6
• GozenYour next number is forced, so a prime is always coming — and on a prime only a square nobody watches will do. · grades 4–6
• ZebraHerds multiply together, so three threes beat one nine — and a stone left on its own throws itself away. · grades 3–6