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Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_031\sol2.py
python
Python
""" Problem 31: https://projecteuler.net/problem=31 Coin sums In England the currency is made up of pound, f, and pence, p, and there are eight coins in general circulation: 1p, 2p, 5p, 10p, 20p, 50p, f1 (100p) and f2 (200p). It is possible to make f2 in the following way: 1xf1 + 1x50p + 2x20p + 1x5p + 1x2p + 3x1p ...
1,569
60
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_032\sol32.py
python
Python
""" We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once; for example, the 5-digit number, 15234, is 1 through 5 pandigital. The product 7254 is unusual, as the identity, 39 x 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital. Fin...
1,636
60
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_033\sol1.py
python
Python
""" Problem 33: https://projecteuler.net/problem=33 The fraction 49/98 is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe that 49/98 = 4/8, which is correct, is obtained by cancelling the 9s. We shall consider fractions like, 30/50 = 3/5, to be trivial exampl...
2,019
73
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_034\sol1.py
python
Python
""" Problem 34: https://projecteuler.net/problem=34 145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145. Find the sum of all numbers which are equal to the sum of the factorial of their digits. Note: As 1! = 1 and 2! = 2 are not sums they are not included. """ from math import factorial DIGIT_FACTORIAL = {...
999
39
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_035\sol1.py
python
Python
""" Project Euler Problem 35 https://projecteuler.net/problem=35 Problem Statement: The number 197 is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime. There are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97. How many circular pr...
2,247
84
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_036\sol1.py
python
Python
""" Project Euler Problem 36 https://projecteuler.net/problem=36 Problem Statement: Double-base palindromes Problem 36 The decimal number, 585 = 10010010012 (binary), is palindromic in both bases. Find the sum of all numbers, less than one million, which are palindromic in base 10 and base 2. (Please note that the ...
1,480
70
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_037\sol1.py
python
Python
""" Truncatable primes Problem 37: https://projecteuler.net/problem=37 The number 3797 has an interesting property. Being prime itself, it is possible to continuously remove digits from left to right, and remain prime at each stage: 3797, 797, 97, and 7. Similarly we can work from right to left: 3797, 379, 37, and 3. ...
3,211
120
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_038\sol1.py
python
Python
""" Project Euler Problem 38: https://projecteuler.net/problem=38 Take the number 192 and multiply it by each of 1, 2, and 3: 192 x 1 = 192 192 x 2 = 384 192 x 3 = 576 By concatenating each product we get the 1 to 9 pandigital, 192384576. We will call 192384576 the concatenated product of 192 and (1,2,3) The same c...
2,458
78
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_039\sol1.py
python
Python
""" Problem 39: https://projecteuler.net/problem=39 If p is the perimeter of a right angle triangle with integral length sides, {a,b,c}, there are exactly three solutions for p = 120. {20,48,52}, {24,45,51}, {30,40,50} For which value of p ≤ 1000, is the number of solutions maximised? """ from __future__ import anno...
1,705
56
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_040\sol1.py
python
Python
""" Champernowne's constant Problem 40 An irrational decimal fraction is created by concatenating the positive integers: 0.123456789101112131415161718192021... It can be seen that the 12th digit of the fractional part is 1. If dn represents the nth digit of the fractional part, find the value of the following expres...
913
46
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_041\sol1.py
python
Python
""" Pandigital prime Problem 41: https://projecteuler.net/problem=41 We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime. What is the largest n-digit pandigital prime that exists? All pandigital numbers ex...
2,073
78
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_042\solution42.py
python
Python
""" The nth term of the sequence of triangle numbers is given by, tn = ½n(n+1); so the first ten triangle numbers are: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ... By converting each letter in a word to a number corresponding to its alphabetical position and adding these values we form a word value. For example, the word...
1,410
48
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_043\sol1.py
python
Python
""" Problem 43: https://projecteuler.net/problem=43 The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it also has a rather interesting sub-string divisibility property. Let d1 be the 1st digit, d2 be the 2nd digit, and so on. In this way, we no...
1,793
67
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_044\sol1.py
python
Python
""" Problem 44: https://projecteuler.net/problem=44 Pentagonal numbers are generated by the formula, Pn=n(3n-1)/2. The first ten pentagonal numbers are: 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ... It can be seen that P4 + P7 = 22 + 70 = 92 = P8. However, their difference, 70 - 22 = 48, is not pentagonal. Find the pai...
1,491
50
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_045\sol1.py
python
Python
""" Problem 45: https://projecteuler.net/problem=45 Triangle, pentagonal, and hexagonal numbers are generated by the following formulae: Triangle T(n) = (n * (n + 1)) / 2 1, 3, 6, 10, 15, ... Pentagonal P(n) = (n * (3 * n - 1)) / 2 1, 5, 12, 22, 35, ... Hexagonal H(n) = n * (2 * n - 1) 1, 6, 15, 28, 45, .....
1,529
60
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_046\sol1.py
python
Python
""" Problem 46: https://projecteuler.net/problem=46 It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square. 9 = 7 + 2 x 12 15 = 7 + 2 x 22 21 = 3 + 2 x 32 25 = 7 + 2 x 32 27 = 19 + 2 x 22 33 = 31 + 2 x 12 It turns out that the conjecture was fals...
2,802
117
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_047\sol1.py
python
Python
""" Combinatoric selections Problem 47 The first two consecutive numbers to have two distinct prime factors are: 14 = 2 x 7 15 = 3 x 5 The first three consecutive numbers to have three distinct prime factors are: 644 = 2² x 7 x 23 645 = 3 x 5 x 43 646 = 2 x 17 x 19. Find the first four consecutive integers to hav...
2,669
113
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_048\sol1.py
python
Python
""" Self Powers Problem 48 The series, 1^1 + 2^2 + 3^3 + ... + 10^10 = 10405071317. Find the last ten digits of the series, 1^1 + 2^2 + 3^3 + ... + 1000^1000. """ def solution(): """ Returns the last 10 digits of the series, 1^1 + 2^2 + 3^3 + ... + 1000^1000. >>> solution() '9110846700' """ ...
486
26
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_049\sol1.py
python
Python
""" Prime permutations Problem 49 The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, (ii) each of the 4-digit numbers are permutations of one another. There are no arithmetic sequences made up of three 1-, 2-, or 3-d...
4,172
154
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_050\sol1.py
python
Python
""" Project Euler Problem 50: https://projecteuler.net/problem=50 Consecutive prime sum The prime 41, can be written as the sum of six consecutive primes: 41 = 2 + 3 + 5 + 7 + 11 + 13 This is the longest sum of consecutive primes that adds to a prime below one-hundred. The longest sum of consecutive primes below on...
2,027
87
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_051\sol1.py
python
Python
""" https://projecteuler.net/problem=51 Prime digit replacements Problem 51 By replacing the 1st digit of the 2-digit number *3, it turns out that six of the nine possible values: 13, 23, 43, 53, 73, and 83, are all prime. By replacing the 3rd and 4th digits of 56**3 with the same digit, this 5-digit number is the fi...
3,137
115
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_052\sol1.py
python
Python
""" Permuted multiples Problem 52 It can be seen that the number, 125874, and its double, 251748, contain exactly the same digits, but in a different order. Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits. """ def solution(): """Returns the smallest positive inte...
803
38
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_053\sol1.py
python
Python
""" Combinatoric selections Problem 53 There are exactly ten ways of selecting three from five, 12345: 123, 124, 125, 134, 135, 145, 234, 235, 245, and 345 In combinatorics, we use the notation, 5C3 = 10. In general, nCr = n!/(r!(n-r)!),where r ≤ n, n! = nx(n-1)x...x3x2x1, and 0! = 1. It is not until n = 23, t...
1,003
45
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_054\sol1.py
python
Python
""" Problem: https://projecteuler.net/problem=54 In the card game poker, a hand consists of five cards and are ranked, from lowest to highest, in the following way: High Card: Highest value card. One Pair: Two cards of the same value. Two Pairs: Two different pairs. Three of a Kind: Three cards of the same value. Str...
14,219
385
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_054\test_poker_hand.py
test
Python
import os from itertools import chain from random import randrange, shuffle import pytest from .sol1 import PokerHand SORTED_HANDS = ( "4S 3H 2C 7S 5H", "9D 8H 2C 6S 7H", "2D 6D 9D TH 7D", "TC 8C 2S JH 6C", "JH 8S TH AH QH", "TS KS 5S 9S AC", "KD 6S 9D TH AD", "KS 8D 4D 9S 4S", # pai...
7,864
229
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_055\sol1.py
python
Python
""" Lychrel numbers Problem 55: https://projecteuler.net/problem=55 If we take 47, reverse and add, 47 + 74 = 121, which is palindromic. Not all numbers produce palindromes so quickly. For example, 349 + 943 = 1292, 1292 + 2921 = 4213 4213 + 3124 = 7337 That is, 349 took three iterations to arrive at a palindrome. A...
2,409
82
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_056\sol1.py
python
Python
""" Project Euler Problem 56: https://projecteuler.net/problem=56 A googol (10^100) is a massive number: one followed by one-hundred zeros; 100^100 is almost unimaginably large: one followed by two-hundred zeros. Despite their size, the sum of the digits in each number is only 1. Considering natural numbers of the fo...
1,050
42
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_057\sol1.py
python
Python
""" Project Euler Problem 57: https://projecteuler.net/problem=57 It is possible to show that the square root of two can be expressed as an infinite continued fraction. sqrt(2) = 1 + 1 / (2 + 1 / (2 + 1 / (2 + ...))) By expanding this for the first four iterations, we get: 1 + 1 / 2 = 3 / 2 = 1.5 1 + 1 / (2 + 1 / 2} ...
1,541
49
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_058\sol1.py
python
Python
""" Project Euler Problem 58:https://projecteuler.net/problem=58 Starting with 1 and spiralling anticlockwise in the following way, a square spiral with side length 7 is formed. 37 36 35 34 33 32 31 38 17 16 15 14 13 30 39 18 5 4 3 12 29 40 19 6 1 2 11 28 41 20 7 8 9 10 27 42 21 22 23 24 25 26 43 44 45 46 4...
2,892
106
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_059\sol1.py
python
Python
""" Each character on a computer is assigned a unique code and the preferred standard is ASCII (American Standard Code for Information Interchange). For example, uppercase A = 65, asterisk (*) = 42, and lowercase k = 107. A modern encryption method is to take a text file, convert the bytes to ASCII, then XOR each byte...
5,019
129
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_062\sol1.py
python
Python
""" Project Euler 62 https://projecteuler.net/problem=62 The cube, 41063625 (345^3), can be permuted to produce two other cubes: 56623104 (384^3) and 66430125 (405^3). In fact, 41063625 is the smallest cube which has exactly three permutations of its digits which are also cube. Find the smallest cube for which exactl...
1,676
63
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_063\sol1.py
python
Python
""" The 5-digit number, 16807=75, is also a fifth power. Similarly, the 9-digit number, 134217728=89, is a ninth power. How many n-digit positive integers exist which are also an nth power? """ """ The maximum base can be 9 because all n-digit numbers < 10^n. Now 9**23 has 22 digits so the maximum power can be 22. Usi...
909
35
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_064\sol1.py
python
Python
""" Project Euler Problem 64: https://projecteuler.net/problem=64 All square roots are periodic when written as continued fractions. For example, let us consider sqrt(23). It can be seen that the sequence is repeating. For conciseness, we use the notation sqrt(23)=[4;(1,3,1,8)], to indicate that the block (1,3,1,8) re...
2,140
77
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_065\sol1.py
python
Python
""" Project Euler Problem 65: https://projecteuler.net/problem=65 The square root of 2 can be written as an infinite continued fraction. sqrt(2) = 1 + 1 / (2 + 1 / (2 + 1 / (2 + 1 / (2 + ...)))) The infinite continued fraction can be written, sqrt(2) = [1;(2)], (2) indicates that 2 repeats ad infinitum. In a similar...
2,672
100
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_067\sol1.py
python
Python
""" Problem Statement: By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23. 3 7 4 2 4 6 8 5 9 3 That is, 3 + 7 + 4 + 9 = 23. Find the maximum total from top to bottom in triangle.txt (right click and 'Save Link/Target As...'), a 15K te...
1,275
49
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_067\sol2.py
python
Python
""" Problem Statement: By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23. 3 7 4 2 4 6 8 5 9 3 That is, 3 + 7 + 4 + 9 = 23. Find the maximum total from top to bottom in triangle.txt (right click and 'Save Link/Target As...'), a 15K te...
1,102
41
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_068\sol1.py
python
Python
""" Project Euler Problem 68: https://projecteuler.net/problem=68 Magic 5-gon ring Problem Statement: Consider the following "magic" 3-gon ring, filled with the numbers 1 to 6, and each line adding to nine. 4 \ 3 / \ 1 - 2 - 6 / 5 Working clockwise, and starting from the group of three with th...
4,146
135
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_069\sol1.py
python
Python
""" Totient maximum Problem 69: https://projecteuler.net/problem=69 Euler's Totient function, φ(n) [sometimes called the phi function], is used to determine the number of numbers less than n which are relatively prime to n. For example, as 1, 2, 4, 5, 7, and 8, are all less than nine and relatively prime to nine, φ(9)...
1,842
67
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_070\sol1.py
python
Python
""" Project Euler Problem 70: https://projecteuler.net/problem=70 Euler's Totient function, φ(n) [sometimes called the phi function], is used to determine the number of positive numbers less than or equal to n which are relatively prime to n. For example, as 1, 2, 4, 5, 7, and 8, are all less than nine and relatively ...
2,790
102
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_071\sol1.py
python
Python
""" Ordered fractions Problem 71 https://projecteuler.net/problem=71 Consider the fraction n/d, where n and d are positive integers. If n<d and HCF(n,d)=1, it is called a reduced proper fraction. If we list the set of reduced proper fractions for d ≤ 8 in ascending order of size, we get: 1/8, 1/7, 1/6, 1/5, 1/4, ...
1,616
49
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_072\sol1.py
python
Python
""" Problem 72 Counting fractions: https://projecteuler.net/problem=72 Description: Consider the fraction, n/d, where n and d are positive integers. If n<d and HCF(n,d)=1, it is called a reduced proper fraction. If we list the set of reduced proper fractions for d ≤ 8 in ascending order of size, we get: 1/8, 1/7, 1/6...
1,477
51
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_072\sol2.py
python
Python
""" Project Euler Problem 72: https://projecteuler.net/problem=72 Consider the fraction, n/d, where n and d are positive integers. If n<d and HCF(n,d)=1, it is called a reduced proper fraction. If we list the set of reduced proper fractions for d ≤ 8 in ascending order of size, we get: 1/8, 1/7, 1/6, 1/5, 1/4, 2/7, ...
1,236
46
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_073\sol1.py
python
Python
""" Project Euler Problem 73: https://projecteuler.net/problem=73 Consider the fraction, n/d, where n and d are positive integers. If n<d and HCF(n,d)=1, it is called a reduced proper fraction. If we list the set of reduced proper fractions for d ≤ 8 in ascending order of size, we get: 1/8, 1/7, 1/6, 1/5, 1/4, 2/7, ...
1,309
52
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_074\sol1.py
python
Python
""" Project Euler Problem 74: https://projecteuler.net/problem=74 The number 145 is well known for the property that the sum of the factorial of its digits is equal to 145: 1! + 4! + 5! = 1 + 24 + 120 = 145 Perhaps less well known is 169, in that it produces the longest chain of numbers that link back to 169; it tur...
2,883
110
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_074\sol2.py
python
Python
""" Project Euler Problem 074: https://projecteuler.net/problem=74 The number 145 is well known for the property that the sum of the factorial of its digits is equal to 145: 1! + 4! + 5! = 1 + 24 + 120 = 145 Perhaps less well known is 169, in that it produces the longest chain of numbers that link back to 169; it tu...
4,904
148
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_075\sol1.py
python
Python
""" Project Euler Problem 75: https://projecteuler.net/problem=75 It turns out that 12 cm is the smallest length of wire that can be bent to form an integer sided right angle triangle in exactly one way, but there are many more examples. 12 cm: (3,4,5) 24 cm: (6,8,10) 30 cm: (5,12,13) 36 cm: (9,12,15) 40 cm: (8,15,17...
2,047
60
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_076\sol1.py
python
Python
""" Counting Summations Problem 76: https://projecteuler.net/problem=76 It is possible to write five as a sum in exactly six different ways: 4 + 1 3 + 2 3 + 1 + 1 2 + 2 + 1 2 + 1 + 1 + 1 1 + 1 + 1 + 1 + 1 How many different ways can one hundred be written as a sum of at least two positive integers? """ def solutio...
1,160
56
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_077\sol1.py
python
Python
""" Project Euler Problem 77: https://projecteuler.net/problem=77 It is possible to write ten as the sum of primes in exactly five different ways: 7 + 3 5 + 5 5 + 3 + 2 3 + 3 + 2 + 2 2 + 2 + 2 + 2 + 2 What is the first value which can be written as the sum of primes in over five thousand different ways? """ from __...
2,080
83
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_078\sol1.py
python
Python
""" Problem 78 Url: https://projecteuler.net/problem=78 Statement: Let p(n) represent the number of different ways in which n coins can be separated into piles. For example, five coins can be separated into piles in exactly seven different ways, so p(5)=7. OOOOO OOOO O OOO OO ...
1,394
63
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_079\sol1.py
python
Python
""" Project Euler Problem 79: https://projecteuler.net/problem=79 Passcode derivation A common security method used for online banking is to ask the user for three random characters from a passcode. For example, if the passcode was 531278, they may ask for the 2nd, 3rd, and 5th characters; the expected reply would be...
2,245
71
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_080\sol1.py
python
Python
""" Project Euler Problem 80: https://projecteuler.net/problem=80 Author: Sandeep Gupta Problem statement: For the first one hundred natural numbers, find the total of the digital sums of the first one hundred decimal digits for all the irrational square roots. Time: 5 October 2020, 18:30 """ import decimal def solu...
1,142
40
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_081\sol1.py
python
Python
""" Problem 81: https://projecteuler.net/problem=81 In the 5 by 5 matrix below, the minimal path sum from the top left to the bottom right, by only moving to the right and down, is indicated in bold red and is equal to 2427. [131] 673 234 103 18 [201] [96] [342] 965 150 630 803 [746] ...
1,560
49
Python
TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_082\sol1.py
python
Python
""" Project Euler Problem 82: https://projecteuler.net/problem=82 The minimal path sum in the 5 by 5 matrix below, by starting in any cell in the left column and finishing in any cell in the right column, and only moving up, down, and right, is indicated in red and bold; the sum is equal to 994. 131 673 [23...
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TheAlgorithms/Python
TheAlgorithms
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All Algorithms implemented in Python
project_euler\problem_085\sol1.py
python
Python
""" Project Euler Problem 85: https://projecteuler.net/problem=85 By counting carefully it can be seen that a rectangular grid measuring 3 by 2 contains eighteen rectangles.  Although there exists no rectangular grid that contains exactly two million rectangles, find the area of the grid with the nearest solution. S...
4,363
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TheAlgorithms/Python
TheAlgorithms
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All Algorithms implemented in Python
project_euler\problem_086\sol1.py
python
Python
""" Project Euler Problem 86: https://projecteuler.net/problem=86 A spider, S, sits in one corner of a cuboid room, measuring 6 by 5 by 3, and a fly, F, sits in the opposite corner. By travelling on the surfaces of the room the shortest "straight line" distance from S to F is 10 and the path is shown on the diagram. ...
4,329
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TheAlgorithms/Python
TheAlgorithms
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All Algorithms implemented in Python
project_euler\problem_087\sol1.py
python
Python
""" Project Euler Problem 87: https://projecteuler.net/problem=87 The smallest number expressible as the sum of a prime square, prime cube, and prime fourth power is 28. In fact, there are exactly four numbers below fifty that can be expressed in such a way: 28 = 22 + 23 + 24 33 = 32 + 23 + 24 49 = 52 + 23 + 24 47 = ...
1,571
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TheAlgorithms/Python
TheAlgorithms
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All Algorithms implemented in Python
project_euler\problem_089\sol1.py
python
Python
""" Project Euler Problem 89: https://projecteuler.net/problem=89 For a number written in Roman numerals to be considered valid there are basic rules which must be followed. Even though the rules allow some numbers to be expressed in more than one way there is always a "best" way of writing a particular number. For e...
3,625
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TheAlgorithms/Python
TheAlgorithms
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All Algorithms implemented in Python
project_euler\problem_091\sol1.py
python
Python
""" Project Euler Problem 91: https://projecteuler.net/problem=91 The points P (x1, y1) and Q (x2, y2) are plotted at integer coordinates and are joined to the origin, O(0,0), to form ΔOPQ.  There are exactly fourteen triangles containing a right angle that can be formed when each coordinate lies between 0 and 2 incl...
1,736
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TheAlgorithms/Python
TheAlgorithms
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All Algorithms implemented in Python
project_euler\problem_092\sol1.py
python
Python
""" Project Euler Problem 092: https://projecteuler.net/problem=92 Square digit chains A number chain is created by continuously adding the square of the digits in a number to form a new number until it has been seen before. For example, 44 → 32 → 13 → 10 → 1 → 1 85 → 89 → 145 → 42 → 20 → 4 → 16 → 37 → 58 → 89 Therefor...
3,186
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TheAlgorithms/Python
TheAlgorithms
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MIT
All Algorithms implemented in Python
project_euler\problem_094\sol1.py
python
Python
""" Project Euler Problem 94: https://projecteuler.net/problem=94 It is easily proved that no equilateral triangle exists with integral length sides and integral area. However, the almost equilateral triangle 5-5-6 has an area of 12 square units. We shall define an almost equilateral triangle to be a triangle for whi...
1,256
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TheAlgorithms/Python
TheAlgorithms
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All Algorithms implemented in Python
project_euler\problem_095\sol1.py
python
Python
""" Project Euler Problem 95: https://projecteuler.net/problem=95 Amicable Chains The proper divisors of a number are all the divisors excluding the number itself. For example, the proper divisors of 28 are 1, 2, 4, 7, and 14. As the sum of these divisors is equal to 28, we call it a perfect number. Interestingly th...
4,498
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TheAlgorithms/Python
TheAlgorithms
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MIT
All Algorithms implemented in Python
project_euler\problem_097\sol1.py
python
Python
""" The first known prime found to exceed one million digits was discovered in 1999, and is a Mersenne prime of the form 2**6972593 - 1; it contains exactly 2,098,960 digits. Subsequently other Mersenne primes, of the form 2**p - 1, have been found which contain more digits. However, in 2004 there was found a massive n...
1,294
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TheAlgorithms/Python
TheAlgorithms
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MIT
All Algorithms implemented in Python
project_euler\problem_099\sol1.py
python
Python
""" Problem: Comparing two numbers written in index form like 2'11 and 3'7 is not difficult, as any calculator would confirm that 2^11 = 2048 < 3^7 = 2187. However, confirming that 632382^518061 > 519432^525806 would be much more difficult, as both numbers contain over three million digits. Using base_exp.txt, a 22K...
1,064
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TheAlgorithms/Python
TheAlgorithms
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MIT
All Algorithms implemented in Python
project_euler\problem_100\sol1.py
python
Python
""" Project Euler Problem 100: https://projecteuler.net/problem=100 If a box contains twenty-one coloured discs, composed of fifteen blue discs and six red discs, and two discs were taken at random, it can be seen that the probability of taking two blue discs, P(BB) = (15/21) x (14/20) = 1/2. The next such arrangemen...
1,324
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TheAlgorithms/Python
TheAlgorithms
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MIT
All Algorithms implemented in Python
project_euler\problem_101\sol1.py
python
Python
""" If we are presented with the first k terms of a sequence it is impossible to say with certainty the value of the next term, as there are infinitely many polynomial functions that can model the sequence. As an example, let us consider the sequence of cube numbers. This is defined by the generating function, u(n) = ...
6,674
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TheAlgorithms/Python
TheAlgorithms
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MIT
All Algorithms implemented in Python
project_euler\problem_102\sol1.py
python
Python
""" Three distinct points are plotted at random on a Cartesian plane, for which -1000 ≤ x, y ≤ 1000, such that a triangle is formed. Consider the following two triangles: A(-340,495), B(-153,-910), C(835,-947) X(-175,41), Y(-421,-714), Z(574,-645) It can be verified that triangle ABC contains the origin, whereas tr...
2,472
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TheAlgorithms/Python
TheAlgorithms
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MIT
All Algorithms implemented in Python
project_euler\problem_104\sol1.py
python
Python
""" Project Euler Problem 104 : https://projecteuler.net/problem=104 The Fibonacci sequence is defined by the recurrence relation: Fn = Fn-1 + Fn-2, where F1 = 1 and F2 = 1. It turns out that F541, which contains 113 digits, is the first Fibonacci number for which the last nine digits are 1-9 pandigital (contain all ...
3,106
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TheAlgorithms/Python
TheAlgorithms
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MIT
All Algorithms implemented in Python
project_euler\problem_107\sol1.py
python
Python
""" The following undirected network consists of seven vertices and twelve edges with a total weight of 243.  The same network can be represented by the matrix below. A B C D E F G A - 16 12 21 - - - B 16 - - 17 20 - - C 12 - - 28 - 31 - D 21 17 28 - 18 19 23 ...
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TheAlgorithms/Python
TheAlgorithms
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MIT
All Algorithms implemented in Python
project_euler\problem_109\sol1.py
python
Python
""" In the game of darts a player throws three darts at a target board which is split into twenty equal sized sections numbered one to twenty.  The score of a dart is determined by the number of the region that the dart lands in. A dart landing outside the red/green outer ring scores zero. The black and cream regions ...
3,157
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TheAlgorithms/Python
TheAlgorithms
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MIT
All Algorithms implemented in Python
project_euler\problem_112\sol1.py
python
Python
""" Problem 112: https://projecteuler.net/problem=112 Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, 134468. Similarly if no digit is exceeded by the digit to its right it is called a decreasing number; for example, 66420. We shall call a pos...
2,783
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TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_113\sol1.py
python
Python
""" Project Euler Problem 113: https://projecteuler.net/problem=113 Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, 134468. Similarly if no digit is exceeded by the digit to its right it is called a decreasing number; for example, 66420. We ...
1,947
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TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_114\sol1.py
python
Python
""" Project Euler Problem 114: https://projecteuler.net/problem=114 A row measuring seven units in length has red blocks with a minimum length of three units placed on it, such that any two red blocks (which are allowed to be different lengths) are separated by at least one grey square. There are exactly seventeen way...
1,659
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TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_115\sol1.py
python
Python
""" Project Euler Problem 115: https://projecteuler.net/problem=115 NOTE: This is a more difficult version of Problem 114 (https://projecteuler.net/problem=114). A row measuring n units in length has red blocks with a minimum length of m units placed on it, such that any two red blocks (which are allowed to be differ...
1,859
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TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_116\sol1.py
python
Python
""" Project Euler Problem 116: https://projecteuler.net/problem=116 A row of five grey square tiles is to have a number of its tiles replaced with coloured oblong tiles chosen from red (length two), green (length three), or blue (length four). If red tiles are chosen there are exactly seven ways this can be done. ...
2,106
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TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_117\sol1.py
python
Python
""" Project Euler Problem 117: https://projecteuler.net/problem=117 Using a combination of grey square tiles and oblong tiles chosen from: red tiles (measuring two units), green tiles (measuring three units), and blue tiles (measuring four units), it is possible to tile a row measuring five units in length in exactly ...
1,590
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TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_119\sol1.py
python
Python
""" Problem 119: https://projecteuler.net/problem=119 Name: Digit power sum The number 512 is interesting because it is equal to the sum of its digits raised to some power: 5 + 1 + 2 = 8, and 8^3 = 512. Another example of a number with this property is 614656 = 28^4. We shall define an to be the nth term of this sequ...
1,289
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TheAlgorithms/Python
TheAlgorithms
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MIT
All Algorithms implemented in Python
project_euler\problem_120\sol1.py
python
Python
""" Problem 120 Square remainders: https://projecteuler.net/problem=120 Description: Let r be the remainder when (a-1)^n + (a+1)^n is divided by a^2. For example, if a = 7 and n = 3, then r = 42: 6^3 + 8^3 = 728 ≡ 42 mod 49. And as n varies, so too will r, but for a = 7 it turns out that r_max = 42. For 3 ≤ a ≤ 1000,...
856
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TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_121\sol1.py
python
Python
""" A bag contains one red disc and one blue disc. In a game of chance a player takes a disc at random and its colour is noted. After each turn the disc is returned to the bag, an extra red disc is added, and another disc is taken at random. The player pays £1 to play and wins if they have taken more blue discs than r...
2,130
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TheAlgorithms/Python
TheAlgorithms
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MIT
All Algorithms implemented in Python
project_euler\problem_122\sol1.py
python
Python
""" Project Euler Problem 122: https://projecteuler.net/problem=122 Efficient Exponentiation The most naive way of computing n^15 requires fourteen multiplications: n x n x ... x n = n^15. But using a "binary" method you can compute it in six multiplications: ...
2,728
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TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_123\sol1.py
python
Python
""" Problem 123: https://projecteuler.net/problem=123 Name: Prime square remainders Let pn be the nth prime: 2, 3, 5, 7, 11, ..., and let r be the remainder when (pn-1)^n + (pn+1)^n is divided by pn^2. For example, when n = 3, p3 = 5, and 43 + 63 = 280 ≡ 5 mod 25. The least value of n for which the remainder first e...
2,399
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TheAlgorithms/Python
TheAlgorithms
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MIT
All Algorithms implemented in Python
project_euler\problem_125\sol1.py
python
Python
""" Problem 125: https://projecteuler.net/problem=125 The palindromic number 595 is interesting because it can be written as the sum of consecutive squares: 6^2 + 7^2 + 8^2 + 9^2 + 10^2 + 11^2 + 12^2. There are exactly eleven palindromes below one-thousand that can be written as consecutive square sums, and the sum o...
1,614
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TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_129\sol1.py
python
Python
""" Project Euler Problem 129: https://projecteuler.net/problem=129 A number consisting entirely of ones is called a repunit. We shall define R(k) to be a repunit of length k; for example, R(6) = 111111. Given that n is a positive integer and GCD(n, 10) = 1, it can be shown that there always exists a value, k, for wh...
1,595
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TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_131\sol1.py
python
Python
""" Project Euler Problem 131: https://projecteuler.net/problem=131 There are some prime values, p, for which there exists a positive integer, n, such that the expression n^3 + n^2p is a perfect cube. For example, when p = 19, 8^3 + 8^2 x 19 = 12^3. What is perhaps most surprising is that for each prime with this pr...
1,250
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TheAlgorithms/Python
TheAlgorithms
220,221
MIT
All Algorithms implemented in Python
project_euler\problem_135\sol1.py
python
Python
""" Project Euler Problem 135: https://projecteuler.net/problem=135 Given the positive integers, x, y, and z, are consecutive terms of an arithmetic progression, the least value of the positive integer, n, for which the equation, x2 - y2 - z2 = n, has exactly two solutions is n = 27: 342 - 272 - 202 = 122 - 92 - 62 =...
1,846
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TheAlgorithms/Python
TheAlgorithms
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MIT
All Algorithms implemented in Python
project_euler\problem_136\sol1.py
python
Python
""" Project Euler Problem 136: https://projecteuler.net/problem=136 Singleton Difference The positive integers, x, y, and z, are consecutive terms of an arithmetic progression. Given that n is a positive integer, the equation, x^2 - y^2 - z^2 = n, has exactly one solution when n = 20: 13...
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TheAlgorithms/Python
TheAlgorithms
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MIT
All Algorithms implemented in Python
project_euler\problem_144\sol1.py
python
Python
""" In laser physics, a "white cell" is a mirror system that acts as a delay line for the laser beam. The beam enters the cell, bounces around on the mirrors, and eventually works its way back out. The specific white cell we will be considering is an ellipse with the equation 4x^2 + y^2 = 100 The section correspondin...
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TheAlgorithms/Python
TheAlgorithms
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All Algorithms implemented in Python
project_euler\problem_145\sol1.py
python
Python
""" Project Euler problem 145: https://projecteuler.net/problem=145 Author: Vineet Rao, Maxim Smolskiy Problem statement: Some positive integers n have the property that the sum [ n + reverse(n) ] consists entirely of odd (decimal) digits. For instance, 36 + 63 = 99 and 409 + 904 = 1313. We will call such numbers reve...
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TheAlgorithms/Python
TheAlgorithms
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MIT
All Algorithms implemented in Python
project_euler\problem_164\sol1.py
python
Python
""" Project Euler Problem 164: https://projecteuler.net/problem=164 Three Consecutive Digital Sum Limit How many 20 digit numbers n (without any leading zero) exist such that no three consecutive digits of n have a sum greater than 9? Brute-force recursive solution with caching of intermediate results. """ def sol...
1,710
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TheAlgorithms/Python
TheAlgorithms
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All Algorithms implemented in Python
project_euler\problem_173\sol1.py
python
Python
""" Project Euler Problem 173: https://projecteuler.net/problem=173 We shall define a square lamina to be a square outline with a square "hole" so that the shape possesses vertical and horizontal symmetry. For example, using exactly thirty-two square tiles we can form two different square laminae: With one-hundred ti...
1,266
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TheAlgorithms/Python
TheAlgorithms
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All Algorithms implemented in Python
project_euler\problem_174\sol1.py
python
Python
""" Project Euler Problem 174: https://projecteuler.net/problem=174 We shall define a square lamina to be a square outline with a square "hole" so that the shape possesses vertical and horizontal symmetry. Given eight tiles it is possible to form a lamina in only one way: 3x3 square with a 1x1 hole in the middle. How...
1,664
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TheAlgorithms/Python
TheAlgorithms
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All Algorithms implemented in Python
project_euler\problem_180\sol1.py
python
Python
""" Project Euler Problem 234: https://projecteuler.net/problem=234 For any integer n, consider the three functions f1,n(x,y,z) = x^(n+1) + y^(n+1) - z^(n+1) f2,n(x,y,z) = (xy + yz + zx)*(x^(n-1) + y^(n-1) - z^(n-1)) f3,n(x,y,z) = xyz*(xn-2 + yn-2 - zn-2) and their combination fn(x,y,z) = f1,n(x,y,z) + f2,n(x,y,z) ...
5,939
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TheAlgorithms/Python
TheAlgorithms
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All Algorithms implemented in Python
project_euler\problem_187\sol1.py
python
Python
""" Project Euler Problem 187: https://projecteuler.net/problem=187 A composite is a number containing at least two prime factors. For example, 15 = 3 x 5; 9 = 3 x 3; 12 = 2 x 2 x 3. There are ten composites below thirty containing precisely two, not necessarily distinct, prime factors: 4, 6, 9, 10, 14, 15, 21, 22, 2...
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TheAlgorithms/Python
TheAlgorithms
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MIT
All Algorithms implemented in Python
project_euler\problem_188\sol1.py
python
Python
""" Project Euler Problem 188: https://projecteuler.net/problem=188 The hyperexponentiation of a number The hyperexponentiation or tetration of a number a by a positive integer b, denoted by a↑↑b or b^a, is recursively defined by: a↑↑1 = a, a↑↑(k+1) = a(a↑↑k). Thus we have e.g. 3↑↑2 = 3^3 = 27, hence 3↑↑3 = 3^27 = ...
1,901
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TheAlgorithms/Python
TheAlgorithms
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MIT
All Algorithms implemented in Python
project_euler\problem_190\sol1.py
python
Python
""" Project Euler Problem 190: https://projecteuler.net/problem=190 Maximising a Weighted Product Let S_m = (x_1, x_2, ..., x_m) be the m-tuple of positive real numbers with x_1 + x_2 + ... + x_m = m for which P_m = x_1 * x_2^2 * ... * x_m^m is maximised. For example, it can be verified that |_ P_10 _| = 4112 (|_ _|...
1,248
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TheAlgorithms/Python
TheAlgorithms
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MIT
All Algorithms implemented in Python
project_euler\problem_191\sol1.py
python
Python
""" Prize Strings Problem 191 A particular school offers cash rewards to children with good attendance and punctuality. If they are absent for three consecutive days or late on more than one occasion then they forfeit their prize. During an n-day period a trinary string is formed for each child consisting of L's (lat...
3,329
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TheAlgorithms/Python
TheAlgorithms
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All Algorithms implemented in Python
project_euler\problem_203\sol1.py
python
Python
""" Project Euler Problem 203: https://projecteuler.net/problem=203 The binomial coefficients (n k) can be arranged in triangular form, Pascal's triangle, like this: 1 1 1 1 2 1 1 3 3 1 1 4 6 4 ...
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TheAlgorithms/Python
TheAlgorithms
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All Algorithms implemented in Python
project_euler\problem_205\sol1.py
python
Python
""" Project Euler Problem 205: https://projecteuler.net/problem=205 Peter has nine four-sided (pyramidal) dice, each with faces numbered 1, 2, 3, 4. Colin has six six-sided (cubic) dice, each with faces numbered 1, 2, 3, 4, 5, 6. Peter and Colin roll their dice and compare totals: the highest total wins. The result i...
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TheAlgorithms
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All Algorithms implemented in Python
project_euler\problem_206\sol1.py
python
Python
""" Project Euler Problem 206: https://projecteuler.net/problem=206 Find the unique positive integer whose square has the form 1_2_3_4_5_6_7_8_9_0, where each “_” is a single digit. ----- Instead of computing every single permutation of that number and going through a 10^9 search space, we can narrow it down conside...
2,256
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TheAlgorithms/Python
TheAlgorithms
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MIT
All Algorithms implemented in Python
project_euler\problem_207\sol1.py
python
Python
""" Project Euler Problem 207: https://projecteuler.net/problem=207 Problem Statement: For some positive integers k, there exists an integer partition of the form 4**t = 2**t + k, where 4**t, 2**t, and k are all positive integers and t is a real number. The first two such partitions are 4**1 = 2**1 + 2 and 4**1.58496...
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TheAlgorithms
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All Algorithms implemented in Python
project_euler\problem_234\sol1.py
python
Python
""" https://projecteuler.net/problem=234 For an integer n ≥ 4, we define the lower prime square root of n, denoted by lps(n), as the largest prime ≤ √n and the upper prime square root of n, ups(n), as the smallest prime ≥ √n. So, for example, lps(4) = 2 = ups(4), lps(1000) = 31, ups(1000) = 37. Let us call an integer...
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