Sandfall

This is an abelian sandpile, run backwards. Every cell started with three grains; a fourth tipped it over, spilling one grain to each neighbour, which could then tip its own neighbours in turn. Any grain that crossed the board's edge is gone for good.

The pips you see are the readings that survived that cascade. Solving means working out where the grains fell from an incomplete record of where the avalanche stopped.

RULES

• Each cell started with exactly 3 grains, before any fell.
• A cell that reaches 4 grains topples: one grain moves to each orthogonal neighbour, with any grain that would leave the board simply lost.
• The visible pips are the readings that survived; cells marked ? had theirs lost.

CONTROLS

• Tap to mark where a grain fell.
• Arrow keys move the cursor; space or enter marks or clears a cell.