이경수 선생님의 수학실험실

Problem 11(Largest product in a grid)In the 20×20 grid below, four numbers along a diagonal line have been marked in red.08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65 52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91 22 31 16 71 51 67 63 89 41 92 36 54 2..

Problem 10(Summation of primes)The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.Find the sum of all the primes below two million. In Python:import time startTime = time.time() primes = [] signPrimes = [] for i in range(1, 2 * pow(10, 6) + 2): signPrimes.append(1) signPrimes[0] = 0 signPrimes[1] = 0 signPrimes[2] = 1 for i in range(2, 2 * pow(10, 6) + 1): if signPrimes[i] == 0: pass else: pri..

Problem 9(Special Pythagorean triplet)A Pythagorean triplet is a set of three natural numbers, a

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..

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..