project euler 250

Ambitious target of solving easiest 250 problems on project euler.

Solved Problems:

1. Problem1|Multiple of 3 or 5

   • You are the 973310th person to have solved this problem.

2. Problem2|Even Fibonacci Numbers

   • You are the 777097th person to have solved this problem.
   • Tweaked problem & conclusion here

3. Problem6|Sum Square Difference

   • 502086th
   • Squares of first N natural numbers = Sum of cubes of first N natural numbers

4. Problem5|Smallest Multiple

   • 499069th
   • LCM when applied to a collection of numbers is commutative, associate & idempotent

5. Problem3|Largest Prime Factor

   • 560060th
   • Input num is > 600Billion => a sieve impl of linear space algo will require 600GB of space. Instead, we chip away at the number by going from smallest factor and repeatedly dividing the number. The final number left gives the result.

6. Problem4|Largest Palindrome Product

   • 495977th
   • All even length palindrome numbers are multiples of 11

7. Problem5|10001st prime

   • 430326th
   • Sieve of eratothenes + Prime Number Theoram: num of primes <n = ~n/logn
   • Alternate Solution: Every prime > 3 can be represented in the form of 6k+-1 i.e. check for only these numbers till sqrt(n) to check for primality.

8. Problem9|Special Pythagorean triplet

   • 366037th
   • Primitive Pythagoream Triplets properties (a=m^2-n^2, b = 2mn, c = m^2+n^2 with a < b < c) can used to optimise the solution