Project Euler Solutions

Problem 1:

Python code:

end = 1000

nums = []

for i in range(1, end):

if i%3==0 or i%==:

nums.append(i)

total = sum(nums)

C++ code:

// problem1.cpp

#include <iostream>

#include <math.h>

#include <time.h>

using namespace std;

int main(){

clock_t tSTart = clock();

int n = 10;

float A = 0;

for (int i = 1; i < 1000; i++) {

if ((i % 3 == 0) || (i % 5 == 0)) {

A += i;

}

}

cout << "A: " << A << '\n';

cout << "Calculation time: " << (double)(clock() - tSTart) / CLOCKS_PER_SEC << " [sec]\n";

}

The sum of multiples of 3 and 5 below 1000 is 233168

Problem 2:

Python code:

fibonacci_list_even = []

max = 4000000

fib_num = 0

num1 = 0

num2 = 1

while fib_num < max:

fib_num = num1+num2

num1 = num2

num2 = fib_num

if fib_num%2==0:

fibonacci_list_even.append(fib_num)

total = sum(fibonacci_list_even)

C++ code:

// problem2.cpp

#include <iostream>

#include <math.h>

#include <time.h>

using namespace std;

int main(){

clock_t tSTart = clock();

int fib_num = 0;

int fib1 = 0;

int fib2 = 1;

int fib_sum = 0;

int max = 4000000;

while (fib_num < max) {

fib_num = fib1 + fib2;

fib1 = fib2;

fib2 = fib_num;

if (fib_num % 2 == 0) {

fib_sum += fib_num;

}

}

cout << "The sum of even Fibonacci numbers below 4 miliion: " << fib_sum << '\n';

cout << "Calculation time: " << (double)(clock() - tSTart) / CLOCKS_PER_SEC << " [sec]\n";

}

The sum of even Fibonacci numbers under 4 million is 4613732

Problem 3:

C++ code:

// problem3.cpp

#include <iostream>

#include <math.h>

#include <time.h>

#include <list>

using namespace std;

bool primeCheck(int n) {

bool isPrime = true;

// 0 and 1 are not prime numbers

if (n == 0 || n == 1) {

isPrime = false;

}

else {

for (int i = 2; i <= n / 2; ++i) {

if (n % i == 0) {

isPrime = false;

break;

}

}

}

return isPrime;

}

int main() {

clock_t tSTart = clock();

int n = 600851475143;

cout << "The Prime Divisors of " << n << " are:\n";

for (int i=1; i<floor(pow(n,0.5)+1); i++) {

if (n % i == 0) {

int div = n / i;

if (primeCheck(div))

cout << div << "\n";

if (primeCheck(i))

cout << i << "\n";

}

}

cout << "Calculation time: " << (double)(clock() - tSTart) / CLOCKS_PER_SEC << " [sec]\n";

}

The answer is 6857

*please note: this code didn't produce the correct answer when I ran it on my laptop because my version of visual studio uses a 32 bit version of windows, leading to overflow.

Problem 4:

Problem 5:

Problem 6:

Problem 7:

Problem 16:

n = 1000

num = 2**n

num_str = str(num)

sum_num = 0

for i in range(len(num_str)):

sum_num += int(num_str[i])

print(sum_num)

the sum of the digits of the number 2^1000 is: 1366

Problem 20:

def fact(x):

if x==0:

ans = 1

else:

ans = x

while x != 1:

x -= 1

ans *= x

return ans

num = fact(100)

num_str = str(num)

sum_num = 0

for i in range(len(num_str)):

sum_num += int(num_str[i])

print(sum_num)

The answer is 648

Problem 25:

F = [1,1]

counter = 2

while True:

x = F[len(F)-1]+F[len(F)-2]

F.append(x)

x_str = str(x)

counter += 1

if len(x_str) > 999:

print(counter)

break

The answer is 4782

Problem 29:

a_l = [2]

b_l = [2]

max_num = 100

for x in range(3, max_num+1):

a_l.append(x)

b_l.append(x)

exp_list = []

for a in a_l:

for b in b_l:

exp_list.append(a**b)

exp_list.sort()

print(len(set(exp_list)))

The answer is 9183

Problem 36:

def is_palindrome(x):

return x == x[::-1]

num_dp = 0

for num in range(10**6):

num_str = str(num)

if is_palindrome(num_str) == True:

bin_num2 = din(num)

binary2 = []

for i in range(2, len(bin_num2)):

binary2.append(int(bin_num2[i]))

if is_palindrome(binary2) == True:

num_dp += num

The sum of double palindromes below 1 million is 872187

Problem 52:

def same_nums(num1, num2):

num1_str = str(num1)

num2_str = str(num2)

if len(num1_str) == len(num2_str):

for i in range(len(num1_str)):

if num1_str[i] not in num2_str or num2_str[i] not in num1_str:

return 0

return num1

else:

return 0

num1 = 1

check = False

while check is False:

num2 = 2*num1

num3 = 3*num1

num4 = 4*num1

num5 = 5*num1

num6v = 6*num1

if same_nums(num1, num2) != 0 and same_nums(num1, num3) != 0 and same_nums(num1, num4) != 0 and same_nums(num1, num5) != 0 and same_nums(num1, num6) != 0:

print(num1)

check = True

num1 += 1

The answer is 142857

Problem 69:

num = 10**6

n_div_phi_max = 0

n_max = 0

for n in range(2, num+1):

relative_prime = []

for i in range(1, n):

coprime_check = gcd(n, i)

if coprime_check ==1:

relative_prime.append(i)

phi = len(relative_prime)

n_div_phi = n/phi

if n_div_phi > n_div_phi_max:

n_div_phi_max = n_div_phi

n_max = n

The answer is 510510

Problem 97:

prime = (28433*(2**7830457))+1

The answer is 8739992577

Problem 112:

def is_bouncy(num):

num = str(num)

num_list = []

nums = []

for i in num:

num_list.append(int(i))

nums.append(int(i))

nums.sort()

if nums == num_list:

return 0

nums.sort(reverse=True)

if nums == num_list:

return 0

return 1

def find(pd):

num = 100

bouncy = 0

while True:

x = is_bouncy(num)

if x == 1:

bouncy += 1

if bouncy => pd:

return num

num += 1

percent_bouncy = 0.99

number = find(percent_bouncy)

The answer is 1587000