mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 21:41:08 +00:00
59 lines
3.1 KiB
Markdown
59 lines
3.1 KiB
Markdown
|
# ProjectEuler
|
|||
|
|
|
|||
|
|
Problems are taken from https://projecteuler.net/.
|
|||
|
|
|
|||
|
|
Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical
|
|||
|
|
insights to solve. Project Euler is ideal for mathematicians who are learning to code.
|
|||
|
|
|
|||
|
|
Here the efficiency of your code is also checked.
|
|||
|
|
I've tried to provide all the best possible solutions.
|
|||
|
|
|
|||
|
|
PROBLEMS:
|
|||
|
|
|
|||
|
|
1. If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3,5,6 and 9. The sum of these multiples is 23.
|
|||
|
|
Find the sum of all the multiples of 3 or 5 below N.
|
|||
|
|
|
|||
|
|
2. Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2,
|
|||
|
|
the first 10 terms will be:
|
|||
|
|
1,2,3,5,8,13,21,34,55,89,..
|
|||
|
|
By considering the terms in the Fibonacci sequence whose values do not exceed n, find the sum of the even-valued terms.
|
|||
|
|
e.g. for n=10, we have {2,8}, sum is 10.
|
|||
|
|
|
|||
|
|
3. The prime factors of 13195 are 5,7,13 and 29. What is the largest prime factor of a given number N?
|
|||
|
|
e.g. for 10, largest prime factor = 5. For 17, largest prime factor = 17.
|
|||
|
|
|
|||
|
|
4. A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99.
|
|||
|
|
Find the largest palindrome made from the product of two 3-digit numbers which is less than N.
|
|||
|
|
|
|||
|
|
5. 2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.
|
|||
|
|
What is the smallest positive number that is evenly divisible(divisible with no remainder) by all of the numbers from 1 to N?
|
|||
|
|
|
|||
|
|
6. The sum of the squares of the first ten natural numbers is,
|
|||
|
|
1^2 + 2^2 + ... + 10^2 = 385
|
|||
|
|
The square of the sum of the first ten natural numbers is,
|
|||
|
|
(1 + 2 + ... + 10)^2 = 552 = 3025
|
|||
|
|
Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 − 385 = 2640.
|
|||
|
|
Find the difference between the sum of the squares of the first N natural numbers and the square of the sum.
|
|||
|
|
|
|||
|
|
7. By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.
|
|||
|
|
What is the Nth prime number?
|
|||
|
|
|
|||
|
|
9. A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
|
|||
|
|
a^2 + b^2 = c^2
|
|||
|
|
There exists exactly one Pythagorean triplet for which a + b + c = 1000.
|
|||
|
|
Find the product abc.
|
|||
|
|
|
|||
|
|
14. The following iterative sequence is defined for the set of positive integers:
|
|||
|
|
n → n/2 (n is even)
|
|||
|
|
n → 3n + 1 (n is odd)
|
|||
|
|
Using the rule above and starting with 13, we generate the following sequence:
|
|||
|
|
13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
|
|||
|
|
Which starting number, under one million, produces the longest chain?
|
|||
|
|
|
|||
|
|
16. 2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.
|
|||
|
|
What is the sum of the digits of the number 2^1000?
|
|||
|
|
20. n! means n × (n − 1) × ... × 3 × 2 × 1
|
|||
|
|
For example, 10! = 10 × 9 × ... × 3 × 2 × 1 = 3628800,
|
|||
|
|
and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27.
|
|||
|
|
Find the sum of the digits in the number 100!
|