https://adnatull.github.io/tags/mathematics/Recent content in Mathematics on Adnatull's Bloghttps://adnatull.github.io/images/logo.jpghttps://adnatull.github.io/images/logo.jpgHugoen-usThu, 08 Feb 2018 23:08:50 +0000https://adnatull.github.io/dev/2018/02/08/the-josephus-problem/Thu, 08 Feb 2018 23:08:50 +0000https://adnatull.github.io/dev/2018/02/08/the-josephus-problem/<h3 id="introduction">Introduction</h3> <p>The <strong>Josephus Problem</strong> is a count-out game which is regarded as a theoretical problem in Computer Science or Mathematics. In this game, <strong>n</strong> people stand in a circle <strong>s</strong> is the starting number of people. <strong>s</strong> is holding a sword where <strong>s</strong> kills <strong>s+k-1</strong>&rsquo;th people from his position and gives his sword to <strong>s+k</strong>&rsquo;th people. Thus <strong>s+k</strong> becomes new <strong>s</strong>.<!-- more --> Going in the same direction this procedure is repeated until one person is left. Remaining one person is marked as a winner. The gif below explains the procedure. Here n = 12, k = 3 &amp; s = 1.</p>