euler
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#Project Euler

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

Project Euler (named after Leonhard Euler) is a website dedicated to a series of computational problems intended to be solved with computer programs. The project attracts adults and students interested in mathematics and computer programming. Participants can track their progress through fourteen achievement levels based on number of problems solved. A special Eulerians level exists to track achievement based on the fastest twenty solvers of recent problems so that newer members can compete without solving older problems.

#Problems

__1 problem__ - *ruby* *go*
>Add all the natural numbers below one thousand that are multiples of 3 or 5.

__2 problem__ - *ruby*
>By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.

__3 problem__ - *ruby*
>Find the largest prime factor of a composite number.

__4 problem__ - *ruby*
>Find the largest palindrome made from the product of two 3-digit numbers.

__5 problem__ - *ruby*
>What is the smallest number divisible by each of the numbers 1 to 20?

__6 problem__ - *ruby*
>What is the difference between the sum of the squares and the square of the sums?

__7 problem__ - *ruby*
>Find the 10001st prime.

__8 problem__ - *ruby*
>Discover the largest product of five consecutive digits in the 1000-digit number.

__9 problem__ - *ruby*
>Find the only Pythagorean triplet, {a, b, c}, for which a + b + c = 1000.

__10 problem__ - *ruby*
>Calculate the sum of all the primes below two million.

__11 problem__ - *ruby*
>What is the greatest product of four adjacent numbers on the same straight line in the 20 by 20 grid?

__12 problem__ - *ruby*
>What is the value of the first triangle number to have over five hundred divisors?

__13 problem__ - *ruby*
>Find the first ten digits of the sum of one-hundred 50-digit numbers.

__14 problem__ - *ruby*
>Find the longest sequence using a starting number under one million.

__15 problem__ - *ruby*
>Starting in the top left corner in a 20 by 20 grid, how many routes are there to the bottom right corner?

__16 problem__ - *ruby*
>What is the sum of the digits of the number 21000?

__18 problem__ - *ruby*
>Find the maximum sum travelling from the top of the triangle to the base.
__20 problem__ - *ruby*
>Find the sum of digits in 100!

__21 problem__ - *ruby*
>Evaluate the sum of all amicable pairs under 10000.

__22 problem__ - *ruby*
>What is the total of all the name scores in the file of first names?

__23 problem__ - *ruby*
>Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.

__24 problem__ - *ruby*
>What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?

__25 problem__ - *ruby*
>What is the first term in the Fibonacci sequence to contain 1000 digits?

__29 problem__ - *ruby*
>How many distinct terms are in the sequence generated by ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?

__30 problem__ - *ruby*
>Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.

__48 problem__ - *ruby*
>Find the last ten digits of 11 + 22 + ... + 10001000.

__67 problem__ - *ruby*
>Using an efficient algorithm find the maximal sum in the triangle?

__81 problem__ - *ruby*
>Find the minimal path sum from the top left to the bottom right by moving right and down.

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