{"id":16202,"date":"2023-02-10T22:46:03","date_gmt":"2023-02-10T17:16:03","guid":{"rendered":"https:\/\/www.interviewbit.com\/blog\/?post_type=web-story&#038;p=16202"},"modified":"2023-02-10T22:46:04","modified_gmt":"2023-02-10T17:16:04","slug":"how-to-solve-the-josephus-problem","status":"publish","type":"web-story","link":"https:\/\/www.interviewbit.com\/blog\/web-stories\/how-to-solve-the-josephus-problem\/","title":{"rendered":"How to Solve the Josephus Problem?"},"content":{"rendered":"<p><html amp=\"\" lang=\"en\"><head><meta charSet=\"utf-8\"\/><meta name=\"viewport\" content=\"width=device-width,minimum-scale=1,initial-scale=1\"\/><script async=\"\" src=\"https:\/\/cdn.ampproject.org\/v0.js\"><\/script><script async=\"\" src=\"https:\/\/cdn.ampproject.org\/v0\/amp-story-1.0.js\" custom-element=\"amp-story\"><\/script><link 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name=\"web-stories-replace-head-end\"\/><\/head><body><amp-story standalone=\"\" publisher=\"InterviewBit\" publisher-logo-src=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/cropped-tumblr-logo.png\" title=\"How to Solve the Josephus Problem?\" poster-portrait-src=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2023\/02\/cropped-Josephus-Problem.jpg\"><amp-story-page id=\"d1e9a7c2-404d-415a-a2eb-eea40554940b\" auto-advance-after=\"7s\"><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#0c2640\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-8713361c-f03a-487f-9a51-a0f98b9ddadb\">\n<div 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src=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2.png\" alt=\"InterviewBit-White-2\" srcSet=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2.png 2130w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-2048x681.png 2048w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-1536x511.png 1536w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-1024x340.png 1024w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-768x255.png 768w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-300x100.png 300w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-150x50.png 150w\" sizes=\"(min-width: 1024px) 20vh, 44vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:5.33981%;top:54.36893%;width:76.69903%;height:25.56634%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 1.2658227848101267% 1.2658227848101267% 1.2658227848101267% 1.2658227848101267%\" id=\"el-95a17566-0eff-4d0a-a9a1-c1eab9f25976\">\n<h1 id=\"how-to-solve-the-josephus-problem\" class=\"fill text-wrapper\" style=\"white-space:pre-line;overflow-wrap:break-word;word-break:break-word;margin:1.3597705696202531% 0;font-family:&quot;Roboto&quot;,sans-serif;font-size:0.809061em;line-height:1;text-align:left;padding:0;color:#000000\"><span><span style=\"font-weight: 700; color: #fff\">How to solve the Josephus Problem?<\/span><\/span><\/h1>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:5.58252%;top:81.06796%;width:91.26214%;height:5.66343%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.5319148936170213% 0.5319148936170213% 0.5319148936170213% 0.5319148936170213% \/ 5.714285714285714% 5.714285714285714% 5.714285714285714% 5.714285714285714%\" id=\"el-cd5e9604-8a06-49c9-ac81-19784a284f87\">\n<h2 id=\"a-puzzling-survival-game\" class=\"fill text-wrapper\" style=\"white-space:pre-line;overflow-wrap:break-word;word-break:break-word;margin:-0.11220079787234044% 0;font-family:&quot;Roboto&quot;,sans-serif;font-size:0.485437em;line-height:1.2;text-align:left;padding:0;color:#000000\"><span><span style=\"font-weight: 700; color: #347eff\">A Puzzling Survival Game<\/span><\/span><\/h2>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:3.8835%;top:90.7767%;width:36.16505%;height:14.23948%;opacity:1\">\n<div 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2130w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-2048x681.png 2048w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-1536x511.png 1536w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-1024x340.png 1024w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-768x255.png 768w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-300x100.png 300w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-150x50.png 150w\" sizes=\"(min-width: 1024px) 20vh, 44vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:6.79612%;top:34.46602%;width:86.40777%;height:35.76052%;opacity:1\">\n<div id=\"anim-6d58e727-4be8-4300-a525-9c00bd15751d\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-558af353-38b5-489d-bd79-1c5f51695a3b\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.5617977528089888% 0.5617977528089888% 0.5617977528089888% 0.5617977528089888% \/ 0.904977375565611% 0.904977375565611% 0.904977375565611% 0.904977375565611%\" id=\"el-01463911-9ace-441d-a6f8-4307552a5552\">\n<h2 id=\"do-you-like-puzzles-and-mathematical-problems-then-get-ready-to-play-the-josephus-game-its-a-game-of-survival-where-the-winner-is-the-last-person-standing\" class=\"fill text-wrapper\" style=\"white-space:pre-line;overflow-wrap:break-word;word-break:break-word;margin:1.5% 0;font-family:&quot;Darker Grotesque&quot;,sans-serif;font-size:0.485437em;line-height:1;text-align:left;padding:0;color:#000000\"><span><span style=\"color: #fff\">Do you like puzzles and mathematical problems?&nbsp;<\/span><\/p>\n<p><span style=\"color: #fff\">Then, get ready to play the Josephus game! It&#8217;s a game of survival where the winner is the last person standing.<\/span><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-page-outlink layout=\"nodisplay\" cta-image=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/10\/Josephus-Problem.png\"><a href=\"https:\/\/www.interviewbit.com\/blog\/josephus-problem\/?utm_source=Ib&amp;utm_medium=webstories&amp;utm_campaign=how-to-solve-josephus-problem\" rel=\"\">Click here<\/a><\/amp-story-page-outlink><\/amp-story-page><amp-story-page id=\"89c46d12-909f-4a7b-b582-777f409a4ac2\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-f647ba22-e78d-4beb-9287-033100a47fad [data-leaf-element=\\\"true\\\"]\",\"keyframes\":{\"transform\":[\"translate(0%, 0%) scale(1.5)\",\"translate(0%, 0%) scale(1)\"]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-802bded1-a355-4a32-991b-23a9b48061d8\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-3428c952-045f-4672-824c-3ba7c7b79fdf\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-45bf76b5-52eb-44df-88ac-8cdbcf759e20\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-fa439f86-8602-4ab9-ba77-14e6a0e0f095\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#f3f3f3\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div id=\"anim-f647ba22-e78d-4beb-9287-033100a47fad\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-76638dd5-e923-4c37-8934-99f03447a159\">\n<div style=\"position:absolute;width:266.31253%;height:100%;left:-83.15627%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/images.unsplash.com\/photo-1573164574397-dd250bc8a598?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw3OHx8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjcwMzM2Mjk2&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=6016&amp;h=4016&amp;fit=max\" alt=\"photography of three women sits beside table inside room during daytime\" srcSet=\"https:\/\/images.unsplash.com\/photo-1573164574397-dd250bc8a598?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw3OHx8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjcwMzM2Mjk2&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=6016&amp;h=4016&amp;fit=max 6016w,https:\/\/images.unsplash.com\/photo-1573164574397-dd250bc8a598?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw3OHx8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjcwMzM2Mjk2&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=4812&amp;h=3212&amp;fit=max 4812w,https:\/\/images.unsplash.com\/photo-1573164574397-dd250bc8a598?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw3OHx8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjcwMzM2Mjk2&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=3609&amp;h=2409&amp;fit=max 3609w,https:\/\/images.unsplash.com\/photo-1573164574397-dd250bc8a598?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw3OHx8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjcwMzM2Mjk2&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=2406&amp;h=1606&amp;fit=max 2406w,https:\/\/images.unsplash.com\/photo-1573164574397-dd250bc8a598?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw3OHx8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjcwMzM2Mjk2&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=1203&amp;h=803&amp;fit=max 1203w,https:\/\/images.unsplash.com\/photo-1573164574397-dd250bc8a598?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw3OHx8c29mdHdhcmUlMjBkZXZlbG9wZXJ8ZW58MHx8fHwxNjcwMzM2Mjk2&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=340&amp;h=227&amp;fit=max 340w\" sizes=\"(min-width: 1024px) 120vh, 267vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<div class=\"element-overlay-area\" style=\"background-color:rgba(0,0,0,0.5)\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"page-background-overlay-area\" style=\"background-color:rgba(0,0,0,0.5)\"><\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-6.31068%;width:43.68932%;height:9.70874%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-90701d05-70b8-48ba-9066-72199e99b3ce\">\n<div style=\"position:absolute;width:100.28251%;height:100%;left:-0.14125%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2.png\" alt=\"InterviewBit-White-2\" srcSet=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2.png 2130w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-2048x681.png 2048w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-1536x511.png 1536w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-1024x340.png 1024w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-768x255.png 768w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-300x100.png 300w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-150x50.png 150w\" sizes=\"(min-width: 1024px) 20vh, 44vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:7.28155%;top:35.11327%;width:85.43689%;height:25.88997%;opacity:1\">\n<div id=\"anim-802bded1-a355-4a32-991b-23a9b48061d8\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-3428c952-045f-4672-824c-3ba7c7b79fdf\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.5681818181818182% 0.5681818181818182% 0.5681818181818182% 0.5681818181818182% \/ 1.25% 1.25% 1.25% 1.25%\" id=\"el-beb9cd08-b670-4372-bebb-c5ab5af8e430\">\n<h2 id=\"consider-n-people-standing-in-a-circle-every-k-th-person-is-eliminated-until-only-one-person-remains-the-task-is-to-find-the-last-person\" class=\"fill text-wrapper\" style=\"white-space:pre-line;overflow-wrap:break-word;word-break:break-word;margin:1.5170454545454544% 0;font-family:&quot;Darker Grotesque&quot;,sans-serif;font-size:0.485437em;line-height:1;text-align:left;padding:0;color:#000000\"><span><span style=\"color: #fff\">Consider N people standing in a circle. Every K-th person is eliminated until only one person remains. The task is to find the last person.<\/span><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:0;top:4.69256%;width:99.51456%;height:11.65049%;opacity:1\">\n<div id=\"anim-45bf76b5-52eb-44df-88ac-8cdbcf759e20\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-fa439f86-8602-4ab9-ba77-14e6a0e0f095\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.4878048780487805% 0.4878048780487805% 0.4878048780487805% 0.4878048780487805% \/ 2.7777777777777777% 2.7777777777777777% 2.7777777777777777% 2.7777777777777777%;background-clip:content-box;background-color:#052258\" id=\"el-474ddcc5-f7c3-4dc9-a20c-3f6b657b137f\">\n<h1 id=\"problem-statement\" class=\"fill text-wrapper\" style=\"white-space:pre-line;overflow-wrap:break-word;word-break:break-word;margin:2.613658536585366% 0;font-family:&quot;Darker Grotesque&quot;,sans-serif;font-size:0.760518em;line-height:0.9;text-align:center;padding:0.975609756097561% 1.951219512195122%;color:#000000\"><span><span style=\"font-weight: 700; color: #3372e0\">Problem Statement<\/span><\/span><\/h1>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-page-outlink layout=\"nodisplay\" cta-image=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/10\/Josephus-Problem.png\"><a href=\"https:\/\/www.interviewbit.com\/blog\/josephus-problem\/?utm_source=Ib&amp;utm_medium=webstories&amp;utm_campaign=how-to-solve-josephus-problem\" rel=\"\">Click here<\/a><\/amp-story-page-outlink><\/amp-story-page><amp-story-page id=\"de3e1538-90d1-44c3-9dc1-e9eb15aea441\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-d8eb9b44-b153-4748-9ea0-9d3cdb7d4d5c\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-238afe0e-991d-4184-ae3e-3a790710ba6d\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-86f36795-4e33-406b-b739-6130cd4cfc01 [data-leaf-element=\\\"true\\\"]\",\"keyframes\":{\"transform\":[\"translate(0%, 0%) scale(1.5)\",\"translate(0%, 0%) scale(1)\"]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-9fd5510a-d5e7-4202-9185-e01934ac6f0c\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-58506074-3b26-47e8-978c-6eb89148a3db\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#d9d9d9\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div id=\"anim-86f36795-4e33-406b-b739-6130cd4cfc01\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-76638dd5-e923-4c37-8934-99f03447a159\">\n<div style=\"position:absolute;width:266.31253%;height:100%;left:-83.15627%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/images.unsplash.com\/photo-1573164574511-73c773193279?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHwxMDh8fHNvZnR3YXJlJTIwZGV2ZWxvcGVyfGVufDB8fHx8MTY3MDMzNjMzMA&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=6016&amp;h=4016&amp;fit=max\" alt=\"photography of people inside room during daytime\" srcSet=\"https:\/\/images.unsplash.com\/photo-1573164574511-73c773193279?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHwxMDh8fHNvZnR3YXJlJTIwZGV2ZWxvcGVyfGVufDB8fHx8MTY3MDMzNjMzMA&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=6016&amp;h=4016&amp;fit=max 6016w,https:\/\/images.unsplash.com\/photo-1573164574511-73c773193279?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHwxMDh8fHNvZnR3YXJlJTIwZGV2ZWxvcGVyfGVufDB8fHx8MTY3MDMzNjMzMA&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=4812&amp;h=3212&amp;fit=max 4812w,https:\/\/images.unsplash.com\/photo-1573164574511-73c773193279?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHwxMDh8fHNvZnR3YXJlJTIwZGV2ZWxvcGVyfGVufDB8fHx8MTY3MDMzNjMzMA&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=3609&amp;h=2409&amp;fit=max 3609w,https:\/\/images.unsplash.com\/photo-1573164574511-73c773193279?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHwxMDh8fHNvZnR3YXJlJTIwZGV2ZWxvcGVyfGVufDB8fHx8MTY3MDMzNjMzMA&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=2406&amp;h=1606&amp;fit=max 2406w,https:\/\/images.unsplash.com\/photo-1573164574511-73c773193279?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHwxMDh8fHNvZnR3YXJlJTIwZGV2ZWxvcGVyfGVufDB8fHx8MTY3MDMzNjMzMA&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=1203&amp;h=803&amp;fit=max 1203w,https:\/\/images.unsplash.com\/photo-1573164574511-73c773193279?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHwxMDh8fHNvZnR3YXJlJTIwZGV2ZWxvcGVyfGVufDB8fHx8MTY3MDMzNjMzMA&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=340&amp;h=227&amp;fit=max 340w\" sizes=\"(min-width: 1024px) 120vh, 267vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<div class=\"element-overlay-area\" style=\"background-color:rgba(0,0,0,0.5)\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"page-background-overlay-area\" style=\"background-color:rgba(0,0,0,0.5)\"><\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-6.31068%;width:43.68932%;height:9.70874%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-ca607fc3-47ce-46f2-be0f-336346011aab\">\n<div style=\"position:absolute;width:100.28251%;height:100%;left:-0.14125%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2.png\" alt=\"InterviewBit-White-2\" srcSet=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2.png 2130w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-2048x681.png 2048w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-1536x511.png 1536w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-1024x340.png 1024w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-768x255.png 768w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-300x100.png 300w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-150x50.png 150w\" sizes=\"(min-width: 1024px) 20vh, 44vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:7.52427%;top:32.68608%;width:84.46602%;height:25.88997%;opacity:1\">\n<div id=\"anim-d8eb9b44-b153-4748-9ea0-9d3cdb7d4d5c\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-238afe0e-991d-4184-ae3e-3a790710ba6d\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.5747126436781609% 0.5747126436781609% 0.5747126436781609% 0.5747126436781609% \/ 1.25% 1.25% 1.25% 1.25%\" id=\"el-91e1f96d-98c1-4640-bbd8-2ceb2f611100\">\n<h2 id=\"we-use-a-recursive-function-that-calculates-the-position-of-the-survivor-in-a-circle-of-n-people-with-every-k-th-person-being-eliminated\" class=\"fill text-wrapper\" style=\"white-space:pre-line;overflow-wrap:break-word;word-break:break-word;margin:1.5344827586206895% 0;font-family:&quot;Darker Grotesque&quot;,sans-serif;font-size:0.485437em;line-height:1;text-align:left;padding:0;color:#000000\"><span><span style=\"color: #fff\">We use a recursive function that calculates the position of the survivor in a circle of N people, with every K-th person being eliminated.<\/span><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:0;top:4.69256%;width:99.51456%;height:18.4466%;opacity:1\">\n<div id=\"anim-9fd5510a-d5e7-4202-9185-e01934ac6f0c\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-58506074-3b26-47e8-978c-6eb89148a3db\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.4878048780487805% 0.4878048780487805% 0.4878048780487805% 0.4878048780487805% \/ 1.7543859649122806% 1.7543859649122806% 1.7543859649122806% 1.7543859649122806%;background-clip:content-box;background-color:#052258\" id=\"el-9b799116-f7f3-4f88-aafc-d52d5a3ec37c\">\n<h1 id=\"approach-1-recursive-approach\" class=\"fill text-wrapper\" style=\"white-space:pre-line;overflow-wrap:break-word;word-break:break-word;margin:2.613658536585366% 0;font-family:&quot;Darker Grotesque&quot;,sans-serif;font-size:0.760518em;line-height:0.9;text-align:center;padding:0.975609756097561% 1.951219512195122%;color:#000000\"><span><span style=\"font-weight: 700; color: #3372e0\">Approach 1-&nbsp;<\/span><br \/>\n<span style=\"font-weight: 700; color: #3372e0\">Recursive Approach<\/span><\/span><\/h1>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-page-outlink layout=\"nodisplay\" cta-image=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/10\/Josephus-Problem.png\"><a href=\"https:\/\/www.interviewbit.com\/blog\/josephus-problem\/?utm_source=Ib&amp;utm_medium=webstories&amp;utm_campaign=how-to-solve-josephus-problem\" rel=\"\">Click here<\/a><\/amp-story-page-outlink><\/amp-story-page><amp-story-page id=\"9e5d6a53-c17c-415a-b590-e6df6d6fd3f4\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-4264c0e2-cccb-4c68-8698-578ee28ef04c [data-leaf-element=\\\"true\\\"]\",\"keyframes\":{\"transform\":[\"translate(0%, 0%) scale(1.5)\",\"translate(0%, 0%) scale(1)\"]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-31662719-7573-4d8c-a64e-0f6fc8ddaf93\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script 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class=\"element-overlay-area\" style=\"background-color:rgba(0,0,0,0.5)\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"page-background-overlay-area\" style=\"background-color:rgba(0,0,0,0.5)\"><\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-6.31068%;width:43.68932%;height:9.70874%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-f24b57dc-e5b9-416a-be22-4a071ebd4794\">\n<div style=\"position:absolute;width:100.28251%;height:100%;left:-0.14125%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2.png\" alt=\"InterviewBit-White-2\" 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id=\"anim-31662719-7573-4d8c-a64e-0f6fc8ddaf93\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-23551c5d-f8e7-417c-94a0-2b2f1a533805\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.5681818181818182% 0.5681818181818182% 0.5681818181818182% 0.5681818181818182% \/ 0.7117437722419928% 0.7117437722419928% 0.7117437722419928% 0.7117437722419928%\" id=\"el-9cdf83be-84a7-4e37-9e13-228230d7f1b6\">\n<h2 id=\"algorithm-1-step-1-if-n-1-return-1-2-step-2-else-return-josephusn-1-k-k-1-n-1-curious-to-see-it-in-action\" class=\"fill text-wrapper\" style=\"white-space:pre-line;overflow-wrap:break-word;word-break:break-word;margin:1.5170454545454544% 0;font-family:&quot;Darker Grotesque&quot;,sans-serif;font-size:0.485437em;line-height:1;text-align:left;padding:0;color:#000000\"><span><span style=\"font-weight: 700; color: #347eff\">Algorithm &#8211;&nbsp;<\/span><\/p>\n<p><span style=\"font-weight: 700; color: #fff\">1. Step 1:<\/span><span style=\"color: #fff\"> If N == 1, return 1.&nbsp;<\/span><\/p>\n<p><span style=\"font-weight: 700; color: #fff\">2. Step 2:<\/span><span style=\"color: #fff\"> Else, return (josephus(N \u2013 1 , K) + K \u2013 1) % N + 1. &nbsp;<\/span><\/p>\n<p><span style=\"color: #347eff\">Curious to see it in action?&nbsp;<\/span><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-page-outlink layout=\"nodisplay\" cta-image=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/10\/Josephus-Problem.png\"><a href=\"https:\/\/www.interviewbit.com\/blog\/josephus-problem\/?utm_source=Ib&amp;utm_medium=webstories&amp;utm_campaign=how-to-solve-josephus-problem\" rel=\"\">Click here<\/a><\/amp-story-page-outlink><\/amp-story-page><amp-story-page id=\"cf434d3e-3132-4b3c-87e0-5ae80860d37a\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-707e39f0-b02b-49ae-b7bf-3be5581e2c5c [data-leaf-element=\\\"true\\\"]\",\"keyframes\":{\"transform\":[\"translate(0%, 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id=\"el-2ad5ac42-0aab-4934-a886-dd828e311d1a\">\n<div style=\"position:absolute;width:100.28251%;height:100%;left:-0.14125%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2.png\" alt=\"InterviewBit-White-2\" srcSet=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2.png 2130w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-2048x681.png 2048w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-1536x511.png 1536w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-1024x340.png 1024w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-768x255.png 768w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-300x100.png 300w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-150x50.png 150w\" sizes=\"(min-width: 1024px) 20vh, 44vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:7.28155%;top:34.46602%;width:85.43689%;height:25.88997%;opacity:1\">\n<div id=\"anim-ba6ae408-a224-422f-9d18-94fb35c3cfed\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-86b9b1ad-e2ac-4873-a1a0-5e172b32b902\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.5681818181818182% 0.5681818181818182% 0.5681818181818182% 0.5681818181818182% \/ 1.25% 1.25% 1.25% 1.25%\" id=\"el-10752c12-70a7-4a16-8ef9-0e5287245dc9\">\n<h2 id=\"simplify-the-josephus-problem-with-a-list-approach-initialize-a-list-of-integers-from-1-to-n-then-repeatedly-remove-the-k-th-element-until-only-one-remains\" class=\"fill text-wrapper\" style=\"white-space:pre-line;overflow-wrap:break-word;word-break:break-word;margin:1.5170454545454544% 0;font-family:&quot;Darker Grotesque&quot;,sans-serif;font-size:0.485437em;line-height:1;text-align:left;padding:0;color:#000000\"><span><span style=\"color: #fff\">Simplify the Josephus problem with a list approach! Initialize a list of integers from 1 to N, then repeatedly remove the K-th element until only one remains.<\/span><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:0;top:4.69256%;width:99.51456%;height:18.4466%;opacity:1\">\n<div id=\"anim-09d70def-1d52-4161-8d58-58e47054fded\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-84cd824f-29d6-45c9-9c6f-d1c03bc63db2\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.4878048780487805% 0.4878048780487805% 0.4878048780487805% 0.4878048780487805% \/ 1.7543859649122806% 1.7543859649122806% 1.7543859649122806% 1.7543859649122806%;background-clip:content-box;background-color:#052258\" id=\"el-48410877-ae3e-4439-b2d8-0dd4db19b77f\">\n<h1 id=\"approach-2-list-method\" class=\"fill text-wrapper\" style=\"white-space:pre-line;overflow-wrap:break-word;word-break:break-word;margin:2.613658536585366% 0;font-family:&quot;Darker Grotesque&quot;,sans-serif;font-size:0.760518em;line-height:0.9;text-align:center;padding:0.975609756097561% 1.951219512195122%;color:#000000\"><span><span style=\"font-weight: 700; color: #3372e0\">Approach 2-&nbsp;<\/span><br \/>\n<span style=\"font-weight: 700; color: #3372e0\">List Method<\/span><\/span><\/h1>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-page-outlink layout=\"nodisplay\" cta-image=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/10\/Josephus-Problem.png\"><a href=\"https:\/\/www.interviewbit.com\/blog\/josephus-problem\/?utm_source=Ib&amp;utm_medium=webstories&amp;utm_campaign=how-to-solve-josephus-problem\" rel=\"\">Click here<\/a><\/amp-story-page-outlink><\/amp-story-page><amp-story-page id=\"015ce16c-01eb-4503-a5fd-c69fd2ace5d2\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-7de70feb-1f98-494d-9839-f7a14e25f022\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-0dac2785-a2bc-49f2-b3f0-85a5bb6615d8\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-a300fb75-1d44-4913-8236-a9c89ed3a82e [data-leaf-element=\\\"true\\\"]\",\"keyframes\":{\"transform\":[\"translate(0%, 0%) scale(1.5)\",\"translate(0%, 0%) scale(1)\"]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script 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class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-07cb1230-628a-4b45-910c-b13bf7f662ea\">\n<div style=\"position:absolute;width:133.38261%;height:100%;left:-16.6913%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/images.unsplash.com\/photo-1582138825658-fb952c08b282?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw0NHx8amF2YSUyMGRldmVsb3BlcnxlbnwwfHx8fDE2NzMwMDg0NzY&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=2707&amp;h=3608&amp;fit=max\" alt=\"man in blue hoodie looking at macbook\" srcSet=\"https:\/\/images.unsplash.com\/photo-1582138825658-fb952c08b282?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw0NHx8amF2YSUyMGRldmVsb3BlcnxlbnwwfHx8fDE2NzMwMDg0NzY&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=2707&amp;h=3608&amp;fit=max 2707w,https:\/\/images.unsplash.com\/photo-1582138825658-fb952c08b282?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw0NHx8amF2YSUyMGRldmVsb3BlcnxlbnwwfHx8fDE2NzMwMDg0NzY&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=2165&amp;h=2886&amp;fit=max 2165w,https:\/\/images.unsplash.com\/photo-1582138825658-fb952c08b282?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw0NHx8amF2YSUyMGRldmVsb3BlcnxlbnwwfHx8fDE2NzMwMDg0NzY&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=1624&amp;h=2165&amp;fit=max 1624w,https:\/\/images.unsplash.com\/photo-1582138825658-fb952c08b282?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw0NHx8amF2YSUyMGRldmVsb3BlcnxlbnwwfHx8fDE2NzMwMDg0NzY&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=1082&amp;h=1442&amp;fit=max 1082w,https:\/\/images.unsplash.com\/photo-1582138825658-fb952c08b282?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw0NHx8amF2YSUyMGRldmVsb3BlcnxlbnwwfHx8fDE2NzMwMDg0NzY&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=541&amp;h=721&amp;fit=max 541w,https:\/\/images.unsplash.com\/photo-1582138825658-fb952c08b282?ixid=MnwxMzcxOTN8MHwxfHNlYXJjaHw0NHx8amF2YSUyMGRldmVsb3BlcnxlbnwwfHx8fDE2NzMwMDg0NzY&amp;ixlib=rb-4.0.3&amp;fm=jpg&amp;w=340&amp;h=453&amp;fit=max 340w\" sizes=\"(min-width: 1024px) 60vh, 134vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<div class=\"element-overlay-area\" style=\"background-color:rgba(0,0,0,0.5)\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"page-background-overlay-area\" style=\"background-color:rgba(0,0,0,0.5)\"><\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-6.31068%;width:43.68932%;height:9.70874%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" 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300w,https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/07\/InterviewBit-White-2-150x50.png 150w\" sizes=\"(min-width: 1024px) 20vh, 44vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:7.28155%;top:36.40777%;width:85.43689%;height:45.46926%;opacity:1\">\n<div id=\"anim-7de70feb-1f98-494d-9839-f7a14e25f022\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-0dac2785-a2bc-49f2-b3f0-85a5bb6615d8\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.5681818181818182% 0.5681818181818182% 0.5681818181818182% 0.5681818181818182% \/ 0.7117437722419928% 0.7117437722419928% 0.7117437722419928% 0.7117437722419928%\" id=\"el-5a80f896-83ce-48d0-b555-413c716f09c1\">\n<h2 id=\"if-n-is-even-all-even-positions-get-deleted-leaving-n-2-the-solution-josephus2-n-2-josephusn-2-1-and-for-n-odd-find-out-by-clicking-here\" class=\"fill text-wrapper\" style=\"white-space:pre-line;overflow-wrap:break-word;word-break:break-word;margin:1.5170454545454544% 0;font-family:&quot;Darker Grotesque&quot;,sans-serif;font-size:0.485437em;line-height:1;text-align:left;padding:0;color:#000000\"><span><span style=\"color: #fff\">If N is even, all even positions get deleted leaving N\/2. The solution?&nbsp;<\/span><\/p>\n<p><span style=\"font-weight: 700; color: #fff\">josephus(2 * N, 2) = josephus(N, 2) &#8211; 1 &nbsp;<\/span><\/p>\n<p><span style=\"color: #347eff\">And for N odd? Find out by clicking here!<\/span><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:0;top:4.69256%;width:99.51456%;height:25.40453%;opacity:1\">\n<div id=\"anim-229a6b85-2bb2-4454-858c-9bde41624be2\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-c8430741-9748-495f-a3a3-d032a5e894c7\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.4878048780487805% 0.4878048780487805% 0.4878048780487805% 0.4878048780487805% \/ 1.2738853503184715% 1.2738853503184715% 1.2738853503184715% 1.2738853503184715%;background-clip:content-box;background-color:#052258\" id=\"el-e5bbfeef-e213-4fbc-8c1d-0f40bc80698b\">\n<h1 id=\"special-case-k2-a-game-changer\" class=\"fill text-wrapper\" style=\"white-space:pre-line;overflow-wrap:break-word;word-break:break-word;margin:2.613658536585366% 0;font-family:&quot;Darker Grotesque&quot;,sans-serif;font-size:0.760518em;line-height:0.9;text-align:center;padding:0.975609756097561% 1.951219512195122%;color:#000000\"><span><span style=\"color: #3372e0\">Special Case:&nbsp;<\/span><br \/>\n<span style=\"font-weight: 700; color: #3372e0\">K=2&nbsp;<\/span><br \/>\n<span style=\"font-weight: 700; color: #3372e0\">A Game Changer!<\/span><\/span><\/h1>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-page-outlink layout=\"nodisplay\" cta-image=\"https:\/\/www.interviewbit.com\/blog\/wp-content\/uploads\/2021\/10\/Josephus-Problem.png\"><a href=\"https:\/\/www.interviewbit.com\/blog\/josephus-problem\/?utm_source=Ib&amp;utm_medium=webstories&amp;utm_campaign=how-to-solve-josephus-problem\" rel=\"\">Click here<\/a><\/amp-story-page-outlink><\/amp-story-page><amp-story-page id=\"936b559d-4dc0-423a-9d89-b4d4ba99b081\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-db71851c-7c7a-4367-9073-bf187d1a3eec\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":600,\"easing\":\"cubic-bezier(0.2, 0.6, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-afc23b4e-29b0-4816-962f-5642ee86abfd\",\"keyframes\":{\"transform\":[\"translate3d(-111.74377%, 0px, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":600,\"easing\":\"cubic-bezier(0.2, 0.6, 0.0, 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0)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" id=\"el-4a501d26-7978-408e-a405-3aa09dd9488d\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-line;overflow-wrap:break-word;word-break:break-word;margin:1.7719780219780208% 0;font-family:&quot;Poppins&quot;,sans-serif;font-size:0.695793em;line-height:1.1;text-align:initial;padding:0;color:#000000\"><span><span style=\"font-weight: 700; color: #fff\">Step Up Your Game with InterviewBit Web Stories<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:7.28155%;top:59.87055%;width:82.52427%;height:13.26861%;opacity:1\">\n<div id=\"anim-be1c6531-0f42-494e-a23f-fdff1826d9c0\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-d728833e-84e8-4333-96ae-192e80b1cf03\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(0px, -621.00265%, 0)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.5882352941176471% 0.5882352941176471% 0.5882352941176471% 0.5882352941176471% \/ 2.4390243902439024% 2.4390243902439024% 2.4390243902439024% 2.4390243902439024%\" id=\"el-059b3c60-05fd-4f35-a8b6-7e0f46822ae8\">\n<h3 id=\"dont-miss-out-on-the-chance-to-upskill-yourself-with-intervewbits-engaging-web-stories\" class=\"fill text-wrapper\" style=\"white-space:pre-line;overflow-wrap:break-word;word-break:break-word;margin:-0.09512867647058793% 0;font-family:&quot;Roboto&quot;,sans-serif;font-size:0.372168em;line-height:1.2;text-align:left;padding:0;color:#000000\"><span><span style=\"color: #fff\">Don&#8217;t miss out on the chance to upskill yourself with IntervewBit&#8217;s engaging web stories.&nbsp;<\/span><\/span><\/h3>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:4.85437%;top:4.36893%;width:19.66019%;height:45.79288%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" id=\"el-e0a006e6-161a-41fd-bd99-ad9adeb2d6a5\">\n<h1 id=\"\" class=\"fill text-wrapper\" style=\"white-space:pre-line;overflow-wrap:break-word;word-break:break-word;margin:49.876543209876516% 0;font-family:&quot;Poppins&quot;,sans-serif;font-size:3.268608em;line-height:1;text-align:initial;padding:0;color:#000000\"><span><span style=\"font-weight: 700; color: #fff\">\u201c<\/span><\/span><\/h1>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-page-outlink layout=\"nodisplay\"><a href=\"https:\/\/www.interviewbit.com\/blog\/web-stories\/?utm_source=Ib&amp;utm_medium=webstories&amp;utm_campaign=unlimited-learning-with-engaging-web-stories\" rel=\"\">SWIPE UP<\/a><\/amp-story-page-outlink><\/amp-story-page><\/amp-story><\/body><\/html><\/p>\n","protected":false},"excerpt":{"rendered":"In this web story, we will show you how to solve Josephus problem. 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