이경수 선생님의 수학실험실

Problem 8(Largest product in a series)The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832. 73167176531330624919225119674426574742355349194934 96983520312774506326239578318016984801869478851843 85861560789112949495459501737958331952853208805511 12540698747158523863050715693290963295227443043557 6689664895044524452316173185640309871112172238311..

Problem 7(10001st prime)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 10 001st prime number? In Python:# PE7 10001st prime import time import math startTime = time.time() order = 1 num = 1 def is_prime(n): if n == 1: return False elif n == 2: return True else: i = 2 while i < math.ceil(math.sqrt(n)) + 1: if n % i == 0: return Fals..

Problem 6(Sum square difference)The sum of the squares of the first ten natural numbers is,12 + 22 + ... + 102 = 385The square of the sum of the first ten natural numbers is,(1 + 2 + ... + 10)2 = 552 = 3025Hence 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 fi..

Problem 5(Smallest multiple)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 by all of the numbers from 1 to 20? In Python:import time startTime = time.time() multiple = 1 temp = 0 for i in range(2, 21): for j in range(2, i+1): temp = multiple while i % j == 0: i = i / j if temp..

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Problem 4(Largest palindrome product)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. In Python:product=0; result=0; num=[] for i in range(100, 1000): for j in range(100, 1000): product=i*j num=str(product) if num==num[::-1]: if product>res..

Problem 3(Largest prime factor)The prime factors of 13195 are 5, 7, 13 and 29.What is the largest prime factor of the number 600851475143 ? In Python:import time start_time = time.time() num = 600851475143 i = 2 while i < (num / 2) + 1: while num % i == 0: num = num / i if num == 1: num = i break i += 1 print(int(num)) print(time.time() - start_time, "Seconds"Run time: 0.0020999908447265625 Seco..

Problem 2(Even Fibonacci numbers)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 four million, find the sum of the even-valued terms. In Python:i=1 limit=4000000 sum=0 def fibonacci(n): if n..