Sudal's Garage

Question: Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n). If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and each of a and b are called amicable numbers.For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142..

Question: n! means n × (n − 1) × ... × 3 × 2 × 1For 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! 문제:n! 이라는 표기법은 n × (n − 1) × ... × 3 × 2 × 1을 뜻합니다.예를 들자면 10! = 10 × 9 × ... × 3 × 2 × 1 = 3628800 이 되는데, 여기서 10!의 각 자리수를 더해 보면 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27 입니다.100! 의 자..

Question: 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 unless it is divisib..

Question: 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 3That 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 56 83 40 80 70 33 41 48..

Question: 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 115 (one hundred and fi..