Solving problems from Project Euler website.
All credit for the formulated problems goes to the Project Euler initiative (projecteuler.net).
Problem #1: Multiples of 3 or 5
If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 1000.
Problem #2: Even Fibonacci numbers
Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.
Problem #3: Largest prime factor
The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143?
Problem #4: Largest palindrome product
A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99. Find the largest palindrome made from the product of two 3-digit numbers.
Problem #5: Smallest multiple
2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?
Problem #6: Sum square difference
The sum of the squares of the first ten natural numbers is: 12+22+...102 = 385.
The square of the sum of the first ten natural numbers is: (1+2+...+10)2=552=3025.
Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is: 3025 - 385 = 2640.
Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.
Problem #7: 10001st prime
By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13. What is the 10 001st prime number?
Problem #8: Largest product in a series
The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832.
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Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?
Problem #9: Special Pythagorean triplet
A Pythagorean triplet is a set of three natural numbers, a < b < c, for which a2 + b2 = c2.
For example, 32 + 42 = 9 + 16 = 25 = 52.
There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.