코딩 연습

A number chain is created by continuously adding the square of the digits in a number to form a new number until it has been seen before For example, 44 → 32 → 13 → 10 → 1 → 1 85 → 89 → 145 → 42 → 20 → 4 → 16 → 37 → 58 → 89 Therefore any chain that arrives at 1 or 89 will become stuck in an endless loop. What is most amazing is that EVERY starting number will eventually arrive at 1 or 89. How ma..

It is well known that if the square root of a natural number is not an integer, then it is irrational. The decimal expansion of such square roots is infinite without any repeating pattern at all. The square root of two is 1.41421356237309504880..., and the digital sum of the first one hundred decimal digits is 475. For the first one hundred natural numbers, find the total of the digital sums of ..

Let \(p(n)\) represent the number of different ways in which \(n\) coins can be separated into piles. For example, five coins can separated into piles in exactly seven different ways, so \(p(5)=7\). OOOOO OOOO O OOO OO OOO O O OO OO O OO O O O O O O O O Find the least value of \(n\) for which \(p(n)\) is divisible by one million. \(n\) 개의 동전을 각기 다른 방법으로 그룹 짓는 방법의 수를 \(p(n)\) 이라 하자. 예를 들어 5개의 동전에..