Two of every number, in a row. The two 3s have three tiles between them; the two 5s, five; and so on down to the ones, side by side. Fill the empty cells so every pair is spaced by its own value.
These arrangements are Langford pairings, named for C. Dudley Langford, who in 1958 watched his small son stack two-of-each coloured blocks and saw one block between the reds, two between the blues, three between the yellows. He asked when it could be done. The answer is exact: a pairing of order n exists if and only if n ≡ 0 or 3 (mod 4) — so 3, 4, 7, 8, 11, 12 … work, and 5, 6, 9, 10 are impossible, no matter how you try (Priday and Davies, 1958–59).
Every day's board is built from a named seed and then proven to have exactly one solution — the site's verifier searches the whole space and confirms a single completion, reachable by pure logic with no guessing. That's the honest edge of this arcade: a normal puzzle app hopes its daily is unique; here it's a checked fact.
The deeper story — how the number of solutions explodes, why the impossible orders are impossible, and the Skolem cousin — lives in the stratum Langford Pairings.