What is ONDA — Ripple Number Puzzle
ONDA is a grid of numbers and a small tray of stones. Drop a stone of value four on a square and it adds four there, three to each square one step away, two at two steps, one at three and nothing beyond. Distance is counted in orthogonal steps, so the wave spreads as a diamond rather than a circle. The numbers on the board are not its contents but what is still missing, and the level is solved when every square reads zero at once.
There is no room to overshoot. Push a square past zero and it turns red with a negative number that says exactly how much wave has to come off again. Waves add wherever they overlap, so one square can be fed by two or three stones, and reading the board is mostly the work of splitting those sums back into their sources. A stone you regret costs nothing but a move: click it and it returns to the tray.
How to play
- Pick a stone from the tray under the board, or press its number key, then click the square where it should land.
- The stone adds its value to that square and one less for every step of distance, out to the edge of its diamond.
- Click a stone already on the board to lift it back into the tray. Undo, restart and hint sit in the bar above the grid, and hints cost points.
- Use every stone and bring all the squares to zero, without pushing any of them below it, to finish the level.
Strategies that work
- Start from the peaks. A square standing exactly one above each of its four neighbours is almost always the seat of a stone of that value, because a lone wave falls by exactly one per step. Place those anchors first and much of the board resolves around them.
- Treat every zero as a wall. A zero square has to stay untouched by every wave, so a stone of value v can never sit closer than v squares to it. On a crowded grid the zeros rule out more placements than the numbers confirm.
- Watch for plateaus and for numbers above your largest stone. A single wave never repeats a value along a straight line and never exceeds the figure on its own stone, so either sign means two waves cross there and the sum must be split first.
- Think about where the wave is spent. A stone in the middle delivers its whole diamond onto the board, while a stone in a corner throws three quarters of it over the edge. A large remaining total wants central stones; a shallow, thin field wants the rim.
- Deduce before you drop, because moving costs more than thinking. Every placement beyond the number of stones takes sixty points off, a hint takes a hundred and fifty, and the clock only bites after about eight seconds per stone.
A little history
ONDA is an original game written for this site, so it has no older version and no inventor to name. Its single rule is a small, visible case of an old mathematical idea, the discrete convolution: one source is spread over a whole space by a fixed kernel, and each point shows the sum of every source after spreading. Here the kernel is the value of the stone minus the taxicab distance, cut off at zero, which is why influence falls away in straight lines and the field a stone makes is a diamond instead of a disc. Reading such a field backwards, from the mixture to the sources that made it, belongs to the same family as deconvolution in signal processing, while the demand that every square land on exactly zero pulls the game towards exact cover, where the pieces must account for the target with nothing left over.
Frequently asked questions
Do I have to use every stone?
Yes. Each level is built by dropping exactly the stones in your tray onto a hidden layout and keeping only the field they produce, so the tray is the solution's shopping list. If squares still show a shortfall once the tray is empty, a stone is in the wrong place rather than missing.
How is the score calculated?
From a thousand points: sixty come off for every placement beyond the number of stones, a hundred and fifty for each hint, and one and a half for every second past a par of eight seconds per stone. The floor is fifty, so a slow solve still counts.
Is my level the same as everyone else's?
Yes. Every board is generated from its level number by a fixed pseudo-random sequence, so level twelve is the same twelve on every device. The daily challenge uses the same machinery: the day's seed picks one level number that everybody plays.
