Skyscrapers Logic vs Euler Grid

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.

Discover Euler Grid, a logic puzzle game inspired by Latin squares and Leonhard Euler’s famous mathematical challenge. Your goal is to place every tile and build a perfectly ordered board. Each tile combines a letter and color with a number and shape. Every letter and every number must appear exactly once in each row and column. The rules are easy to learn, but every larger board requires more focus, strategy, and deduction. PROGRESS THROUGH SEVEN CHALLENGES Start with the 3×3 board and advance through the 4×4, 5×5, 7×7, 8×8, 9×9, and 10×10 orders. You will also discover why order 6 is a famous mathematical exception. KEY FEATURES • Seven boards with increasing difficulty. • Gameplay based on Latin squares and Greco-Latin squares. • Tiles identified by letters, colors, numbers, and shapes. • Clear visual detection of repeated values in rows and columns. • Smart hints to help you find your next move. • Undo and reset options for complete control of the board. • Automatic saving for games in progress. • A performance-based star system. • Game Center leaderboards for the 5×5, 7×7, 8×8, 9×9, and 10×10 boards. • Available in English and Spanish. • A polished landscape interface designed for clear and comfortable play. BEAT YOUR BEST SCORES Every tile placement counts as one attempt, and each hint adds an extra attempt. Complete every board using as few attempts as possible, improve your personal records, and climb the Game Center leaderboards. PLAY AT YOUR OWN PACE Study the board, correct your moves, and search for the perfect arrangement without pressure. Your progress is saved automatically, allowing you to continue whenever you are ready. If you enjoy Sudoku, logic puzzles, mathematical games, and strategic challenges, Euler Grid offers an original and rewarding test for your mind. Can you master every order and become a grandmaster of Latin squares?