Skyscrapers Logic

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.