project_euler/README.markdown

 #My solutions to Project Euler 's website

[Project Euler](http://projecteuler.net/) is a website containing lots of problems aiming at being solved.
I play around with them in order to sharpen my algorithm skills.

This is always challenging to solve problems on paper and fantastic to come up with an algorithmic solution.
I use Python for its simplicity. Simple Python code is very similar to paper solution, and fast to implement.

Each script runs by itself and contains one of several functions that directly solve the function. Thus, running a script should give you the answer directly.

The script are named as e_problemnumber_inc. The higher the inc, the finer my solution.

Here is a list of all already solved problems, with a one line explanation.
Should be used in order to help future reuse of code :)

1 - Add all the natural numbers below one thousand that are multiples of 3 or 5. - 0.011 <br />
2 - By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms. - 0.011 <br />
3 - Find the largest prime factor of a composite number. - < 1 sec <br />
4 - Find the largest palindrome made from the product of two 3-digit numbers. - 0.790 <br />
5 - What is the smallest number divisible by each of the numbers 1 to 20? - 4.102 <br />
6 - What is the difference between the sum of the squares and the square of the sums? - 0.013 <br />
7 - Find the 10001st prime. - too long <br />
8 - Discover the largest product of five consecutive digits in the 1000-digit number. - 0.045 <br />
9 - Find the only Pythagorean triplet, {a, b, c}, for which a + b + c = 1000. (a^2 + b^2 = c^2) - 1.500 <br />
10 - Calculate the sum of all the primes below two million. - too long <br />
11 - What is the greatest product of four adjacent numbers on the same straight line in the 20 by 20 grid? - 0.048 <br />
12 - What is the value of the first triangle number to have over five hundred divisors? - too long <br />
13 - Find the first ten digits of the sum of one-hundred 50-digit numbers. - 0.012 <br />
14 - Find the longest sequence using a starting number under one million. - too long <br />
15 - Starting in the top left corner in a 20 by 20 grid, how many routes are there to the bottom right corner? - 0.012 <br />
16 - What is the sum of the digits of the number 2^1000? - 0.012 <br />
17 - How many letters would be needed to write all the numbers in words from 1 to 1000? - 0.012 <br />
18 - Find the maximum sum travelling from the top of the triangle to the base. - 0.012 <br />
19 - How many Sundays fell on the first of the month during the twentieth century? - 0.088 <br />
20 - Find the sum of digits in 100! - 0.031 <br />
21 - Evaluate the sum of all amicable pairs under 10000. (d(a) = b, d(b) = a) - 9.100 <br />
22 - What is the total of all the name scores in the file of first names? - 0.082 <br />
23 - Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers. - _too long_ <br />
24 - What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9? - too long <br />
25 - What is the first term in the Fibonacci sequence to contain 1000 digits? - 0.741 <br />
26 - Find the value of d < 1000 for which 1/d contains the longest recurring cycle. < 5 sec <br />
27 - Find a quadratic formula that produces the maximum number of primes for consecutive values of n. - too long <br />
28 - What is the sum of both diagonals in a 1001 by 1001 spiral? - < 1 sec <br />
29 - How many distinct terms are in the sequence generated by ab for 2  a  100 and 2  b  100? - < 1 sec <br />
30 - Find the sum of all the numbers that can be written as the sum of fifth powers of their digits. - < 3 sec <br />
31 - Investigating combinations of English currency denominations. - < 1 sec <br />
33 - Discover all the fractions with an unorthodox cancelling method. < 1 sec <br />
34 - Find the sum of all numbers which are equal to the sum of the factorial of their digits. - 30 sec - 16 sec  <br />
35 - How many circular primes are there below one million? <br />
36 - Find the sum of all numbers less than one million, which are palindromic in base 10 and base 2. - 0.933 <br />
37 - Find the sum of all eleven primes that are both truncatable from left to right and right to left. < 1 min <br />
38 - What is the largest 1 to 9 pandigital that can be formed by multiplying a fixed number by 1, 2, 3, ... ? < 1 sec <br />
39 - If p is the perimeter of a right angle triangle, {a, b, c}, which value, for p <= 1000, has the most solutions? - 1min<br />
41 - What is the largest n-digit pandigital prime that exists? < 5 min <br />
42 - Using words.txt, a 16K text file containing nearly two-thousand common English words, how many are triangle words? - < 1 sec <br />
45 - Find the next triangle number that is also pentagonal and hexagonal. - < 1 sec <br />
46 - What is the smallest odd composite that cannot be written as the sum of a prime and twice a square? - < 6 sec <br />
48 - Find the last ten digits of 1^1 + 2^2 + ... + 1000^1000. - 0.053 <br />
52 - Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits. - 2min <br />
53 - How many values of C(n,r), for 1 <= n <= 100, exceed one-million? - < 1 sec <br />
67 - Using an efficient algorithm find the maximal sum in the triangle? - 0.027 <br />

**In progress: **

43 - Find the sum of all pandigital numbers with an unusual sub-string divisibility property. <br />
47 - Find the first four consecutive integers to have four distinct primes factors. <br />
97 - Find the last ten digits of the non-Mersenne prime: 28433 × 2^7830457 + 1. <br />

**WARNING : Spoil inside for those who want to solve problems by themselves :)**

## Contact

I would enjoy having feedback if you try to solve euler's problems too :).
Feel free to mail me for any comment or request.

You can contact me at julien at lengrand dot fr, or on my [current website](http://www.lengrand.fr)

Last update : 5/6/2012