이경수 선생님의 수학실험실

problem18 (Maximum path sum I) 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 of the triangle below: 75 95 64 17 47 82 18 35 87 10 20 04 82 47 65 19 01 23 75 03 34 88 02 77 73 07 63 67 99 65 04 28 06 16 70 92 41 41 26 ..

problem17 (Number letter counts) If the numbers 1 to 5 are written out in words: one, two, three, four, five, then there are 3 + 3 + 5 + 4 + 4 = 19 letters used in total.If all the numbers from 1 to 1000 (one thousand) inclusive were written out in words, how many letters would be used? NOTE: Do not count spaces or hyphens. For example, 342 (three hundred and forty-two) contains 23 letters and 1..

Problem 13(Large sum)Work out the first ten digits of the sum of the following one-hundred 50-digit numbers.37107287533902102798797998220837590246510135740250 46376937677490009712648124896970078050417018260538 74324986199524741059474233309513058123726617309629 91942213363574161572522430563301811072406154908250 23067588207539346171171980310421047513778063246676 89261670696623633820136378418383684..

Problem 12(Highly divisible triangular number)The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...Let us list the factors of the first seven triangle numbers: 1: 1 3: 1,3 6: 1,2,3,6 10: 1,2,5,10 15: 1,3,5,15 21: 1,3,7,21 28: 1,2,4,7,14,..

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 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..