Project Euler Solutions

“Project Euler exists to encourage, challenge, and develop the skills and enjoyment of anyone with an interest in the fascinating world of mathematics.”

Mathematical problems that require both programming skills and mathematical insight to solve efficiently.

🎯 My Philosophy

Each solution demonstrates:

  • Elegant Python code using modern language features
  • Mathematical understanding of the underlying concepts
  • Performance optimization through smart algorithms
  • Multiple approaches from brute force to mathematical insights
  • Real-world patterns applicable beyond the problem

📚 Problems by Theme

🔢 Number Theory & Arithmetic

Fundamental mathematical concepts and number properties.

Problem 001 • Multiples of 3 and 5
Modular arithmetic and boolean logic optimization

Problem 003 • Largest Prime Factor
Prime factorization using specialized libraries

Problem 005 • Smallest Multiple
Least Common Multiple with functional programming

Problem 007 • 10001st Prime
Efficient prime number generation algorithms

Problem 009 • Special Pythagorean Triplet
Constraint-based optimization and number relationships

Problem 010 • Summation of Primes
Prime sieves and mathematical bounds

Problem 029 • Distinct Powers
Set theory and automatic deduplication

∞ Sequences & Series

Infinite mathematical sequences and their properties.

Problem 002 • Even Fibonacci Numbers
Generator functions with itertools.takewhile

Problem 025 • 1000-digit Fibonacci Number
Iterator composition and exponential growth

Problem 012 • Highly Divisible Triangular Number
Triangular sequences and divisor counting

🔍 Pattern Recognition & Optimization

Problems requiring clever bounds and search strategies.

Problem 004 • Largest Palindrome Product
String manipulation with optimized search bounds

Problem 006 • Sum Square Difference
Mathematical formulas vs computational approaches

🏗️ Computational Challenges

Large numbers and algorithmic efficiency.

Problem 016 • Power Digit Sum
Python’s arbitrary precision integer arithmetic

Problem 020 • Factorial Digit Sum
Working with extremely large factorials

⭐ Solution Highlights

Most Pythonic

1
2

# Problem 6: Mathematical elegance in one line
sum(range(101)) ** 2 - sum(x**2 for x in range(101))

Most Creative Logic

1
2

# Problem 1: Boolean arithmetic trick
sum(x for x in range(1_000) if (x % 5) * (x % 3) == 0)

Best Library Usage

1
2

# Problem 3: Leveraging specialized tools
max(primes.factorise(600_851_475_143))

Most Functional

1
2

# Problem 5: Pure functional composition
reduce(lcm, range(1, 21))

Most Mathematical

1
2

# Problem 25: Iterator composition with mathematical bounds
first_true(enumerate(fibonacci()), pred=lambda p: p[1] >= 10**999)[0]

🛠️ Technical Arsenal

Python Features Mastered

  • Generator expressions for memory efficiency
  • Type hints for code clarity
  • Functional programming with reduce(), map(), filter()
  • String manipulation and numeric conversions
  • Set operations for deduplication
  • Iterator protocols and lazy evaluation

Libraries Utilized

  • primePy → Prime number operations and factorization
  • itertools → Advanced iteration patterns (takewhile, dropwhile)
  • more-itertools → Extended iteration utilities (first_true)
  • functools → Higher-order functions (reduce)
  • typing → Static type checking

Mathematical Concepts

  • Modular arithmetic and divisibility rules
  • Prime numbers and factorization algorithms
  • Fibonacci sequences and golden ratio properties
  • Combinatorics and counting principles
  • Number theory patterns and relationships

🎓 Recommended Learning Path

Beginners (⭐)

Start here to build foundational skills:

  1. Problem 001 → Learn modular arithmetic
  2. Problem 006 → Mathematical formula translation
  3. Problem 016 → Working with large numbers

Intermediate (⭐⭐)

Ready for more complex patterns:

  1. Problem 002 → Generator functions
  2. Problem 004 → Optimization techniques
  3. Problem 005 → Functional programming

Advanced (⭐⭐⭐)

Challenge yourself with sophisticated approaches:

  1. Problem 025 → Iterator composition
  2. Problem 009 → Constraint optimization
  3. Problem 029 → Set-based algorithms

📈 Progress Tracker

Problems Solved: 13 / ∞
Techniques Mastered: Prime generation, Fibonacci algorithms, Iterator patterns, Set operations
Next Targets: Dynamic programming, Graph algorithms, Advanced number theory

Ready to dive in? Start with Problem 001 or explore any theme that interests you!