Samon: Designing a Zen Garden Raking Puzzle

Full design for a one-stroke sand-raking puzzle game: a novice monk walks into a dry garden and must rake his way back out to the gate. Solver experiments show the bare rule is loose (1.5 million rakings of a 7×7 garden), but scoring by turns recovers the traditional ripple and wave patterns, and a 'wide rake' rule forbidding U-turns in open sand yields unique, garden-like solutions. Covers rules, mechanics, progression, level generation & grading, interface (including hints that are proofs about the player's own route), presentation, a production plan, and prior art, with a playable prototype.

Raking a Zen dry garden is a chore with the shape of a puzzle: a novice who walks into the sand leaves footprints, and must rake his way back out to the gate without crossing his own lines or raking anything twice. We design Samon (“sand patterns”), a puzzle game built on that rule: the player draws one stroke from the gate covering every cell of sand; the monk walks it in, sets down the rake, and walks backwards out, revealing the pattern.

We formalize gardens as grid graphs and rakings as Hamiltonian paths ending at the gate, show that “walk in, rake out” and the simpler “mirror raking” are exactly equivalent (so the interface can be “draw from the gate”), and test candidate mechanics on thousands of random gardens with an exact solver, a constraint-programming optimizer, and a deductive difficulty grader.

The bare rule is loose: an empty 7×7 garden with a corner gate has 1,510,446 valid rakings, and random stone layouts are mostly either unsolvable (often by checkerboard parity) or wide open. Scoring by turns fixes the slack without new rules: in that 7×7 garden only 66 rakings reach the minimum (“par”) of 12 turns, and par rakings in lightly-stoned gardens tend to be the traditional motifs of parallel lines and rings around stones. A single physical rule, the wide rake (no U-turn in open sand; set the rake down against a stone or wall), collapses gardens to a handful of rakings, often exactly one, and in about half of the calm-looking unique gardens that one is also a par raking of the unrestricted garden: in one 8×8 garden it picks out the only U-turn-free raking among 12 par rakings of 6,310,226. Ripple stones and wave bands, the obvious “pattern” constraints, add texture but not tightness; given grooves pin down unique answers with ~5–8 clues, and pebbles that say only “straight here” or “turn here” need more clues (a median of 11 against 7) but make nearly every garden a lookahead puzzle.

The resulting design has 7 worlds, each adding one rule (shown by a before-and-after pair of small gardens, the second raked once by the monk as a demonstration); free gardens scored against a proven par with Opus Magnum-style histograms; strict gardens with unique, graceful answers; hints that are proofs about the player’s own route (it can still reach par; it can still be finished; or it cannot, and here is the nearest footprint to step back to); a daily garden that can be raked only once; a classical poem as the reward for every raked garden, after which the next garden fades in; a heightfield sand renderer and a free-raking practice garden; a level pipeline whose yields and difficulty distribution we measure; and a production plan with pass/fail criteria. A playable prototype implements most of it, with the whole campaign of 148 gardens and their poems: play it below.

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Sound on Volume Haptics on

静

original

Turns0 Par0

Step back Restore Start over Ask the abbot Watch Rake Next garden

PracticeNo goal

Rake Stones 3 tines Smooth

Assists Preview grooves Checkerboard Cut-off sand

[Drag the monk in from the gate and cover every cell of sand without crossing your path; when you let go, he sets down his rake and walks backwards out, raking. Tap a footprint to step back to it, or the gate to start over; after raking, tap any cell to walk back to it. Fewer turns is calmer: rake at par for the abbot's seal. Each raking brings a poem, then the next garden. Keyboard: arrows walk, Backspace steps back, R starts over, H asks the abbot, Enter goes on.]

[Drag anywhere to rake. With Stones selected, tap to place a stone or lift one; the sand under a stone keeps whatever was there. Smooth rakes the garden flat again.]