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Mastering Dosun-Fuwari: Gravity & Buoyancy Strategy

Published by Nikoli, Dosun-Fuwari is one of the most playful puzzles in the Japanese catalog, simulating the natural physics of heavy iron spheres and light helium balloons.

The Laws of Buoyancy & Mass

  • Room Quota: Each room must contain exactly 1 Iron Ball (\(\bullet\)) and 1 Balloon (\(\circ\)).
  • Iron Ball Gravity: An iron ball cannot hover in empty space. It must sink straight down to the floor, onto a solid wall, or onto an object beneath it.
  • Balloon Lift: A balloon cannot linger in mid-air without support. It rises to the ceiling, beneath a solid wall, or beneath an object above it.
  • No Side-by-Side Clashes: Two circles (whether ball or balloon) can never be adjacent horizontally. Vertical stacking is completely legal!

Deduction Techniques

Inspect narrow rooms that only touch the ceiling or floor at a single cell: if a room has only one cell in the top row, the balloon must float there! Check horizontal exclusions: placing a circle in cell \((r, c)\) immediately rules out \((r, c - 1)\) and \((r, c + 1)\).