Suguru
Fill every outlined block of k cells with the digits 1..k, so that no two equal digits touch — not even diagonally. No rows, no columns: the block and the neighborhood are the whole rulebook. Click a cell, then type or tap a digit.
Suguru is Sudoku with the rows and columns stripped away — what is
left is a pile of tiny all-different problems (the blocks)
glued together by one local rule (equal digits never touch). That
gives the solver two sound rule sets. The singles
are what a person scans for: a cell down to its last candidate, a
digit down to its last home in a block. The
witness rule is what a machine does: enumerate every
way a block can still be filled — at most 5! = 120 — and keep only
what all witnesses agree on. The trick is that a block's witnesses
also fire outward: if every remaining fill pins digit
d somewhere next to an outside cell, that cell can never be
d. Two blank cells over an untouched domino already know
they are not 1 and not 2. The Hint button names whichever
rule fires first, singles before witnesses.
Measured over 100 boards per size: singles alone finish
11% of 6×6 boards and 0% of 8×8 —
and when they stall it is essentially at the start, 3.7 blanks in.
The witness rule is load-bearing from the first moves. The generator
has its own measured surprise: partition the grid by growing regions
through uniformly random frontier cells and only
3% of 8×8 partitions admit any solution at all;
biasing growth toward compact blobs lifts that to
14%. Every board here is carved to a unique
solution and kept only if the witness rules can finish it without
branching — the Hint button never runs dry on a fresh board. Both
rule sets are cross-checked against an independent brute-force
solver: sound rules must agree on solution counts, and a
disagreement is how an unsound rule gets caught.