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Adds information about how I solve problem. 
Puts too long solutions in bold.
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julien Lengrand-Lambert
2012-10-16 22:20:53 +03:00
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#My solutions to Project Euler 's website
# 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.
**[Project Euler](http://projecteuler.net/)** is a website containing lots of problems aiming at being solved.
This is always challenging to solve problems on paper and fantastic to come up with an algorithmic solution.
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.
Each script runs by itself and will directly pop the solution out.
The script are named as e_problemnumber_inc. The higher the inc, the finer my solution.
The scripts are named as e_problemnumber_inc. The higher the inc, the finer the 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 :)
**Note :** I try to get my solutions within a one minute timeframe. What I want here is to solve problems, not get them running as fast as possible.
So you may find some of the code here quite ugly. And this is the case :). Why optimize something that completely fits its purpose ? ;)
## Problems solved
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 />
@@ -22,11 +27,11 @@ Should be used in order to help future reuse of code :)
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 />
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 />
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 />
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 />
@@ -35,18 +40,18 @@ Should be used in order to help future reuse of code :)
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 />
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 />
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 />
35 - How many circular primes are there below one million? - **too long** <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 />
@@ -60,13 +65,11 @@ Should be used in order to help future reuse of code :)
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: **
## 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 :)**
97 - Find the last ten digits of the non-Mersenne prime: 28433 <EFBFBD> 2^7830457 + 1. <br />
## Contact
@@ -75,4 +78,4 @@ 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
Last update : 16/10/2012