{"id":29259,"date":"2023-01-06T14:17:13","date_gmt":"2023-01-06T08:47:13","guid":{"rendered":"https:\/\/jassweb.com\/solved\/solved-count-numbers-where-three-first-digits-equal-last-three\/"},"modified":"2023-01-06T14:17:13","modified_gmt":"2023-01-06T08:47:13","slug":"solved-count-numbers-where-three-first-digits-equal-last-three","status":"publish","type":"post","link":"https:\/\/jassweb.com\/solved\/solved-count-numbers-where-three-first-digits-equal-last-three\/","title":{"rendered":"[Solved] Count numbers where three first digits equal last three"},"content":{"rendered":"<p> [ad_1]<br \/>\n<\/p>\n<div id=\"answer-42270931\" class=\"answer js-answer accepted-answer js-accepted-answer\" data-answerid=\"42270931\" data-parentid=\"42270303\" data-score=\"3\" data-position-on-page=\"1\" data-highest-scored=\"1\" data-question-has-accepted-highest-score=\"1\" itemprop=\"acceptedAnswer\" itemscope itemtype=\"https:\/\/schema.org\/Answer\">\n<div class=\"post-layout\">\n<div class=\"votecell post-layout--left\"><\/div>\n<div class=\"answercell post-layout--right\">\n<div class=\"s-prose js-post-body\" itemprop=\"text\">\n<p>To count all the values where the first three digits equals the last three digits. (As you solution suggests)<\/p>\n<p>You can calculate the range for i4, i5 and the value i6 which makes this much faster.<\/p>\n<pre><code>int count = 0;\nfor (int i1 = 0; i1 &lt;= 9; i1++) {\n    for (int i2 = 0; i2 &lt;= 9; i2++) {\n        for (int i3 = 0; i3 &lt;= 9; i3++) {\n            int sum = i1 + i2 + i3;\n            for (int i4 = Math.max(0, sum - 18); i4 &lt;= Math.min(9, sum); i4++) {\n                int min5 = Math.max(0, sum - i4 - 9);\n                int max5 = Math.min(9, sum - i4);\n                if (min5 &lt;= max5) \/\/ one solution for i6 each\n                    count += max5 - min5 + 1;\n            }\n        }\n    }\n}\nSystem.out.println(count);\n<\/code><\/pre>\n<p>prints the same answer as your solution;<\/p>\n<pre><code>55252\n<\/code><\/pre>\n<p>This is a further optimisation, it recognises that the order of the first three digits doesn&#8217;t matter.<\/p>\n<pre><code>int count = 0;\nfor (int i1 = 0; i1 &lt;= 9; i1++) {\n    for (int i2 = 0; i2 &lt;= i1; i2++) {\n        for (int i3 = 0; i3 &lt;= i2; i3++) {\n            int different = ((i1 != i2)?1:0) + ((i1 != i3)?1:0) + ((i2 != i3)?1:0);\n            int combinations = different == 0 ? 1 : different == 2 ? 3 : 6;\n            int sum = i1 + i2 + i3;\n            for (int i4 = Math.max(0, sum - 18); i4 &lt;= Math.min(9, sum); i4++) {\n                int min5 = Math.max(0, sum - i4 - 9);\n                int max5 = Math.min(9, sum - i4);\n                if (min5 &lt;= max5) \/\/ one solution each\n                    count += combinations * (max5 - min5 + 1);\n            }\n        }\n    }\n}\nSystem.out.println(count);\n<\/code><\/pre>\n<p>What this does is say 123 or 132 or 213 or 231 or 312 or 321 have the same number of solutions. 111 has a factor of 1, 112 has a factor of 3 and 123 has a factor of 6.<\/p>\n<\/p><\/div>\n<div class=\"mt24\"><\/div>\n<\/div>\n<p>            <span class=\"d-none\" itemprop=\"commentCount\">4<\/span> <\/p><\/div>\n<\/div>\n<p>[ad_2]<\/p>\n<p>solved Count numbers where three first digits equal last three <\/p>\n","protected":false},"excerpt":{"rendered":"<p>[ad_1] To count all the values where the first three digits equals the last three digits. (As you solution suggests) You can calculate the range for i4, i5 and the value i6 which makes this much faster. int count = 0; for (int i1 = 0; i1 &lt;= 9; i1++) { for (int i2 = &#8230; <a title=\"[Solved] Count numbers where three first digits equal last three\" class=\"read-more\" href=\"https:\/\/jassweb.com\/solved\/solved-count-numbers-where-three-first-digits-equal-last-three\/\" aria-label=\"More on [Solved] Count numbers where three first digits equal last three\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[320],"tags":[323,468],"class_list":["post-29259","post","type-post","status-publish","format-standard","hentry","category-solved","tag-java","tag-permutation"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>[Solved] Count numbers where three first digits equal last three - JassWeb<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/jassweb.com\/solved\/solved-count-numbers-where-three-first-digits-equal-last-three\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"[Solved] Count numbers where three first digits equal last three - JassWeb\" \/>\n<meta property=\"og:description\" content=\"[ad_1] To count all the values where the first three digits equals the last three digits. 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