코딩 연습

A bag contains one red disc and one blue disc. In a game of chance a player takes a disc at random and its color is noted. After each turn the disc is returned to the bag, an extra red disc is added, and another disc is taken at random. The player pays £1 to play and wins if they have taken more blue discs than red discs at the end of the game. If the game is played for four turns, the probabili..

Let \(r\) be the remainder when \((a-1)^n +(a+1)^n\) is divided by \(a^2\). For example, if \(a=7\) and \(n=3\), then \(r=42: \; 6^3 +8^3 = 728 \equiv 42 \; \rm mod\; 49\). And as \(n\) varies, so too will \(r\), but for \(a=7\) it turns out that \(r_{\rm max} =42\). For \(3 \le a \le 1000\), find \(\sum r_{\rm max}\). \((a-1)^n + (a+1)^n\) 을 \(a^2\) 으로 나누었을 때의 나머지를 \(r\) 라고 하자. 예를 들어, \(a=7\) 이..

Using all of the digits 1 through 9 and concatenating them freely to form decimal integers, different sets can be formed. Interestingly with the set {2, 5, 47, 89, 631}, all of the elements belonging to it are prime. How many distinct sets containing each of the digits one through nine exactly once contain only prime elements? 1 부터 9까지 모든 자연수들을 한 번씩만 사용하여 자연수들을 만든다면 여러 가지 가능성이 있다. 예를 들어, 집합 {2, ..