How the puzzles are made

Every 8flowy board — free play, daily, Journey — comes out of the same generator, and every one ships with the same certificate: exactly one solution, proven by machine. Here's how that works, in plain language.

Step 1: carve the grid into pipes

A valid flow solution is just the grid partitioned into snaking, non-crossing pipes that cover every square. So we build the answer first: the generator lays a single random path that visits every square of the grid (a Hamiltonian path, shuffled by a technique called backbiting until it's thoroughly random), then cuts it into segments at least three squares long. Each segment becomes one pipe; its two ends become that color's dots. Coverage is perfect by construction.

Step 2: prove it's the only answer

Knowing a solution isn't enough — the dots must admit no other network. A solver searches for every way to route the colors: it extends pipes square by square, pruning any line of search where a color can no longer reach its partner, an empty region gets sealed off, or an empty square is starved of open sides. If it finds a second solution, the board is rejected.

Sparse boards (few pairs) are rarely unique by luck, so the generator works top-down: it starts from a dense cut that's almost always unique, then repeatedly merges neighbouring pipes — making the board sparser and harder — keeping each merge only if the solver still proves uniqueness. When no merge survives, the board is as lean as this layout allows.

Step 3: measure the difficulty

The tier on the board is measured, not requested. We walk the unique solution pipe by pipe and count plausible wrong turns: alternative moves that are legal and survive the quick sanity checks a careful human makes. That count, blended with pipe sparsity and the longest pipe, and normalized per board size, gives the 1–100 score and its tier. If a board generated "hard" measures easy, it's labeled easy — and free play keeps generating until it finds you a genuine one. Details on the ratings page.

The daily and the Journey

Daily boards come from a pre-built calendar: thousands of candidates are generated offline, only hard/expert survivors are kept, and each date's board is chosen for looks as well — symmetric, well-spread dots score higher. The week ramps NYT-style: gentler hard boards on Monday, the meanest expert on Sunday. Journey levels are generated against a fixed 200-slot schedule of sizes and tiers, then re-validated one final time before shipping.

Why this matters to you

Because it means deduction always works. Every "it must go this way, or that square dies" argument you make is sound — there is never a second answer lurking to invalidate your logic, and never a board that needs a lucky guess. If you ever find a board that seems to break this promise, report it; it's the bug we take most seriously.