Number Cascade — Kakuro-style puzzle with a directional flow rule

How Number Cascade works

Each puzzle has a few dark "stones" placed on the board, each with a target number. Around every stone is a connected group of empty "water cells" — that's the cascade. Your job is to place a digit (1–9) in every water cell such that:

The digits in a cascade sum to the stone's target.
The digits in a cascade are all different.
(Optional) In Flow mode, the digits strictly increase (or decrease) as you move away from the stone along the cascade.

Why this is different from standard Kakuro

Standard Kakuro only enforces sum and distinct-digit constraints. Number Cascade adds a directional ordering rule that turns many "ambiguous" Kakuro puzzles into unique-solution puzzles — and makes the visual metaphor of water flowing out from a stone actually match the math. Cascades that satisfy the sum but not the flow are wrong.

Difficulty progression

Easy — 3 small cascades, 2–3 cells each, targets 4–10.
Medium — 3–4 cascades, 3 cells each, targets 6–15.
Hard — 4 cascades, mix of L and line shapes, targets 10–23.
Expert — 5 cascades including cross shapes, targets 12–30, strictest flow.

Strategies we found useful in testing

Start with the cascade that has the smallest target. Fewest combinations to try.
In Flow Ascending mode, the digit next to the stone is always the smallest in the cascade. That alone often solves small cascades.
If a cascade has 3 cells and target 10, the only valid ascending triples are (1,2,7), (1,3,6), (1,4,5), (2,3,5). The flow rule narrows it fast.
Use one hint per puzzle. The hint reveals a constraint, not the answer.

Known limitations

Puzzle generation is procedural — there is no curated daily puzzle. If you want a hand-designed one, ping us.
The "Flow Descending" mode is harder for many players because intuition usually assumes ascending. That's a feature, not a bug.
There's no undo history beyond "Clear selected cell". We don't store move history to keep the page lightweight.

About Number Cascade

Number Cascade started as a thought experiment: what if Kakuro had a directional rule? Most Kakuro puzzles have a single solution because the sum-and-distinct constraints are tight enough. But the cascade rule adds a third constraint that — surprisingly — often makes puzzles easier to solve, because it eliminates combinations that the sum rule alone couldn't rule out.

We chose the metaphor of "stones" (anchors with target sums) and "water cells" (fillable cells that flow outward) deliberately. The visual matches the math: ascending flow = water spreading and slowing; descending flow = water converging and accelerating. It gives the puzzle a tactile feel that pure Kakuro lacks.

The hardest design decision was shape variety. We started with only straight-line cascades and found the puzzles felt repetitive. Adding L, T, and cross shapes doubled the design space but required careful generator tuning so every puzzle has a unique solution.

Privacy on Number Cascade

Number Cascade stores your settings and stats only in your browser's localStorage. No game data is sent to any server. Puzzle generation happens entirely in your browser.

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Disclaimer

Number Cascade is a casual logic puzzle for entertainment. It is not a substitute for professional advice, diagnosis, or treatment of any cognitive condition. The site is provided "as is" without warranty of any kind. External links (e.g., Google Ads Settings) are not under our control.