이경수 선생님의 수학실험실

problem19 (Counting Sundays) You are given the following information, but you may prefer to do some research for yourself.1 Jan 1900 was a Monday.Thirty days has September, April, June and November. All the rest have thirty-one, Saving February alone, Which has twenty-eight, rain or shine. And on leap years, twenty-nine.A leap year occurs on any year evenly divisible by 4, but not on a century u..

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..

problem16 (Power digit sum) 215 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.What is the sum of the digits of the number 21000?In Python: # Power digit sum import time startTime = time.time() strNum = str(pow(2,1000)) numList = [int(num) for num in strNum] print(sum(numList)) endTime = time.time() print(endTime - startTime, "seconds") Run time: 0.0006120204925537109 seconds In Jav..

Problem 15(Lattice paths)Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.How many such routes are there through a 20×20 grid? In Python:#PE14 Longest Collatz sequenceimport timestart_time = time.time()lenChain = []for num in range(2, pow(10, 6)): i = 0 while num > 1: i += 1 if num % 2 == 0: nu..

Problem 14(Longest Collatz sequence)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 → 1It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet..

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,..