Skyscrapers Logic vs Limnering

Skyscrapers — A Mathematical Logic Puzzle Skyscrapers is a deterministic logic puzzle based on the mathematical concept of Latin squares, enhanced with edge visibility constraints derived from combinatorial optimization. Game Mechanics: • Grid Size: N×N (4×4, 5×5, or 6×6) • Domain: Fill each cell with integers 1 through N • Constraint 1: Latin Square — each integer appears exactly once per row and column • Constraint 2: Visibility Clues — edge numbers indicate count of visible buildings from that direction • Visibility Function: f(sequence) = count of elements where value[i] > max(value[0..i-1]) Difficulty Architecture: • Easy (4×4): Clue retention rate ~80%. Optimal for learning constraint propagation techniques. • Medium (5×5): Clue retention rate ~60%. Balanced complexity requiring multi-step logical deduction. • Hard (6×6): Clue retention rate ~40%. Advanced difficulty demanding systematic elimination strategies. Analytical Features: • Performance Tracking: Best completion time recorded per difficulty tier • Game Count: Total solved puzzles tracked per difficulty level • Auto-Save System: State persistence via UserDefaults with 500ms debounce • Undo Stack: Up to 100 reversible operations • Notes System: Candidate digit annotation for hypothesis testing • Conflict Detection: Real-time row/column duplicate and clue violation highlighting Technical Specifications: • Platform: iOS 16+ (iPhone, portrait orientation only) • Framework: Pure SwiftUI, zero third-party dependencies • Architecture: MVVM pattern with reactive state management • Performance: O(N) visibility calculation, deterministic puzzle generation • Privacy: 100% offline. No network access, no analytics, no data collection. Target Audience: Engineers, mathematicians, data scientists, and analytical thinkers who appreciate deterministic puzzles with no randomness in solution paths. If you value Sudoku, nonograms, or constraint satisfaction problems, this app delivers rigorous logical challenges.

Paint one page a day. By Christmas, you will have a whole illuminated year. Limnering is a quiet, parchment styled daily puzzle that puts you in the seat of a medieval manuscript painter. Each morning a fresh hand designed page appears in your studio: a saint's portrait, a giant decorative initial, a bestiary creature, a margin drollery, a biblical scene, or a Lindisfarne style carpet page. Tap a region to fill it with the pigment of your choice. Save the page to your year long codex. Come back tomorrow for another. Twelve historical pigments wait in the tray: Lapis lazuli ultramarine, the most expensive medieval pigment, reserved for the Virgin's robe. Vermillion, ground from cinnabar, the bright red of blood and royalty. Gold leaf, beaten foil burnished onto the page for haloes and the figure of Christ. Verdigris, copper acetate, beautiful and corrosive. Malachite, the safe and stable green from copper ore. Indigo, fermented from Indigofera leaves, cheaper than ultramarine. Woad, the European blue, even cheaper. Saffron, hand picked crocus stigmas, used for yellow highlights. Lead white, toxic but bright opaque, the medieval flesh ground. Bone black, charred bones, the scribe's ink and outline color. Madder lake, a cool plant red layered over warmer reds for royal robes. Orpiment, brilliant arsenic yellow, fatal to grind without ventilation. Forty hand designed patterns ship at launch, grouped into six sections: Eight saint portraits with halo, robe, attribute, and flesh. Six decorative initial letters with knotwork interior and marginal vine. Eight marginalia pages: knight and snail, dancing rabbits, monkey trumpet, owl scribe, ape doctor, fox preaching, hare hunting hound, cockerel joust. Four biblical scenes in silhouette: Nativity, Annunciation, Last Supper, Crucifixion. Six bestiary creatures: unicorn, manticore, basilisk, gryphon, leviathan, pelican. Eight geometric Insular carpet pages: four corners, cross of the scribe, rosette, checker field, vesica weave, eight fold knot, star of the north, spiral quadrants. A monastic accuracy score quietly rewards you for following the iconographic conventions a medieval illuminator was taught: gold for haloes, ultramarine for Mary, malachite for foliage, lead white for flesh, vermillion for martyr's robes. The Scriptorium inside the app explains every rule, every pigment, and the source it would have come from. Your scoring history is saved in the codex. There is no time pressure. There is no fail state. There is no system to chase. There is just paint, and parchment, and the soft pluck of a lute when you set down a color. The soundtrack is generated procedurally on device. Three voices model a contemplative monastic chamber piece: an organ drone in the Hypodorian mode, a soft lute pluck for each pigment you apply, and a recorder counterpoint that briefly wells up whenever you satisfy an iconographic rule. No audio files are bundled with the app. Limnering ships with twenty achievements, a yearly codex grid for every UTC day, a sandbox mode that unlocks every pattern from the first launch, accessibility options for reduced motion, dyslexic friendly font, and high contrast outlines, and local SwiftData persistence for the codex. No subscriptions. No in app purchases. No expansion packs. No tracking. No analytics. No accounts. No third party SDKs. Thank you for reading.