Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, 134468. Similarly if no digit is exceeded by the digit to its right it is called a decreasing number; for example, 66420. We shall call a positive integer …
An irrational decimal fraction is created by concatenating the positive integers: 0.123456789101112131415161718192021… It can be seen that the 12th digit of the fractional part is 1. If dn represents the nth digit of the fractional part, find the value of the following expression. d1 × d10 × d100 × d1000 …
Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits: 1634 = 14 + 64 + 34 + 44 8208 = 84 + 24 + 04 + 84 9474 = 94 + 44 + 74 + 44 As 1 = 14 is not a sum it is not included. The sum …
This program generates the intersection, union, relative composition, cross product, and power set, of given input (which generates the sets the operations are performed on. ///////////////////////////////////////////////////////////////////////////////// #include <iostream> #include <vector> #include <algorithm> #include <iterator> #include <sstream> //////////////////////////////////////////////////////////////////////////////// std::vector<std::string> createSet(void); // creates set from user input std::vector<std::string> getIntersection(std::vector<std::string> set_A, std::vector<std::string> set_B); …
//////////////////////////////////////////////////////////////////////////////// #include <iostream> #include <math> //////////////////////////////////////////////////////////////////////////////// void numberQuery(unsigned long long &a, unsigned long long &n, unsigned long long &m); unsigned long long powertworesidual(unsigned long long a, unsigned long long n, unsigned long long m); unsigned long long nonpowertworesidual(unsigned long long a, unsigned long long n, unsigned long long m); //////////////////////////////////////////////////////////////////////////////// …
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 …
The series, 11 + 22 + 33 + … + 1010 = 10405071317. Find the last ten digits of the series, 11 + 22 + 33 + … + 10001000. This problem was solved easily with Python, due to arbitrary length constraints on numbers. import math foo = 1 total …
A permutation is an ordered arrangement of objects. For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. The lexicographic permutations of 0, 1 and 2 are: 012 021 102 …
The Fibonacci sequence is defined by the recurrence relation: Fn = Fn−1 + Fn−2, where F1 = 1 and F2 = 1. Hence the first 12 terms will be: F1 = 1 F2 = 1 F3 = 2 F4 = 3 F5 = 5 F6 = 8 F7 = 13 …
A perfect number is a number for which the sum of its proper divisors is exactly equal to the number. For example, the sum of the proper divisors of 28 would be 1 + 2 + 4 + 7 + 14 = 28, which means that 28 is a perfect …