{"id":409,"date":"2025-12-16T16:19:18","date_gmt":"2025-12-16T03:19:18","guid":{"rendered":"https:\/\/thesudoku.com\/blog\/?page_id=409"},"modified":"2026-07-13T16:20:49","modified_gmt":"2026-07-13T04:20:49","slug":"last-remaining-number","status":"publish","type":"page","link":"https:\/\/thesudoku.com\/blog\/last-remaining-number\/","title":{"rendered":"Last Remaining Number"},"content":{"rendered":"\n<div class=\"wp-block-group content-wrapper has-base-background-color has-background has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\" style=\"min-height:90vh;margin-top:var(--wp--preset--spacing--40);margin-bottom:var(--wp--preset--spacing--40);padding-top:0;padding-bottom:0\">\n<div class=\"wp-block-group has-global-padding is-layout-constrained wp-container-core-group-is-layout-b5150c35 wp-block-group-is-layout-constrained\" style=\"padding-top:var(--wp--preset--spacing--40);padding-right:var(--wp--preset--spacing--40);padding-bottom:0;padding-left:var(--wp--preset--spacing--40)\">\n<p class=\"is-style-default\" style=\"font-size:clamp(14px, 0.875rem + ((1vw - 3.2px) * 0.392), 18px);font-style:normal;font-weight:700\"><a href=\"https:\/\/thesudoku.com\/blog\/sudoku-rules\/\" data-type=\"page\" data-id=\"73\">&lt; Back<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-group has-global-padding is-layout-constrained wp-container-core-group-is-layout-8dd13e6d wp-block-group-is-layout-constrained\" style=\"padding-right:var(--wp--preset--spacing--60);padding-left:var(--wp--preset--spacing--60)\">\n<p class=\"is-style-text-display is-style-text-display--1\" style=\"font-size:clamp(17.905px, 1.119rem + ((1vw - 3.2px) * 0.99), 28px);font-style:normal;font-weight:800\">How to Find the Last Remaining Number<\/p>\n\n\n\n<p>The <strong>Last Remaining Number<\/strong> strategy\u2014widely known in the Sudoku community as a <strong>Sole Candidate<\/strong>\u2014is a powerful and essential technique for solving puzzles.<\/p>\n\n\n\n<p>While the <em>Last Free Cell<\/em> strategy focuses on scanning a single nearly complete row, column, or block, this technique requires a broader view. You need to look at the <strong>intersection<\/strong> of all three units at once to figure out what belongs in a specific empty cell.<\/p>\n\n\n\n<div class=\"wp-block-group has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\" style=\"padding-top:var(--wp--preset--spacing--20);padding-bottom:var(--wp--preset--spacing--20)\">\n<figure class=\"wp-block-image aligncenter size-full is-resized is-style-default\" style=\"margin-top:var(--wp--preset--spacing--30);margin-right:0;margin-bottom:0;margin-left:0\"><img loading=\"lazy\" decoding=\"async\" width=\"697\" height=\"697\" src=\"https:\/\/thesudoku.com\/blog\/wp-content\/uploads\/2025\/12\/Group-7516.png\" alt=\"Sudoku grid before applying the Last Remaining Number technique\" class=\"wp-image-413\" style=\"object-fit:cover;width:349px;height:auto\" srcset=\"https:\/\/thesudoku.com\/blog\/wp-content\/uploads\/2025\/12\/Group-7516.png 697w, https:\/\/thesudoku.com\/blog\/wp-content\/uploads\/2025\/12\/Group-7516-300x300.png 300w, https:\/\/thesudoku.com\/blog\/wp-content\/uploads\/2025\/12\/Group-7516-150x150.png 150w\" sizes=\"auto, (max-width: 697px) 100vw, 697px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" style=\"margin-top:var(--wp--preset--spacing--40);margin-bottom:var(--wp--preset--spacing--20)\"\/>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\">The Logic Behind the Strategy<\/h2>\n\n\n\n<p>In Sudoku, a single cell is always part of three distinct units simultaneously:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>One horizontal row<\/li>\n\n\n\n<li>One vertical column<\/li>\n\n\n\n<li>One 3&#215;3 block<\/li>\n<\/ul>\n\n\n\n<p>Because a number cannot repeat within any of these units, every digit that already exists in the intersecting row, column, or block is instantly eliminated as a possibility for that specific cell.<\/p>\n\n\n\n<p>When you eliminate eight out of the nine possible digits, the <strong>last remaining number<\/strong> becomes the only logical answer.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Step-by-Step Example<\/h2>\n\n\n\n<p>Have a look at the highlighted cell in the image below<\/p>\n\n\n\n<div class=\"wp-block-group has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\" style=\"padding-top:var(--wp--preset--spacing--20);padding-bottom:var(--wp--preset--spacing--20)\">\n<figure class=\"wp-block-image aligncenter size-full is-resized is-style-default\" style=\"margin-top:var(--wp--preset--spacing--30);margin-right:0;margin-bottom:0;margin-left:0\"><img loading=\"lazy\" decoding=\"async\" width=\"697\" height=\"697\" src=\"https:\/\/thesudoku.com\/blog\/wp-content\/uploads\/2025\/12\/Group-7517.png\" alt=\"Identifying the last remaining number for a given cell\" class=\"wp-image-414\" style=\"object-fit:cover;width:349px;height:auto\" srcset=\"https:\/\/thesudoku.com\/blog\/wp-content\/uploads\/2025\/12\/Group-7517.png 697w, https:\/\/thesudoku.com\/blog\/wp-content\/uploads\/2025\/12\/Group-7517-300x300.png 300w, https:\/\/thesudoku.com\/blog\/wp-content\/uploads\/2025\/12\/Group-7517-150x150.png 150w\" sizes=\"auto, (max-width: 697px) 100vw, 697px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" style=\"margin-top:var(--wp--preset--spacing--40);margin-bottom:var(--wp--preset--spacing--20)\"\/>\n<\/div>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>Pick a target cell:<\/strong> Choose an empty cell that seems to be surrounded by a lot of numbers.<\/li>\n\n\n\n<li><strong>Scan the intersections:<\/strong> Look at all the numbers that already exist in the target cell&#8217;s row, its column, and its 3&#215;3 block.<\/li>\n\n\n\n<li><strong>Count the eliminated digits:<\/strong> In our example, if we look across the intersecting units, we can see that the numbers <strong>1, 2, 3, 4, 6, 7, 8, and 9<\/strong> are already taken.<\/li>\n\n\n\n<li><strong>Place the final number:<\/strong> Since 8 out of 9 options are blocked, only one number can logically go into this cell. The last remaining number is <strong>5<\/strong>.<\/li>\n<\/ol>\n\n\n\n<div class=\"wp-block-group has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\" style=\"padding-top:var(--wp--preset--spacing--20);padding-bottom:var(--wp--preset--spacing--20)\">\n<figure class=\"wp-block-image aligncenter size-full is-resized is-style-default\" style=\"margin-top:var(--wp--preset--spacing--30);margin-right:0;margin-bottom:var(--wp--preset--spacing--30);margin-left:0\"><img loading=\"lazy\" decoding=\"async\" width=\"697\" height=\"697\" src=\"https:\/\/thesudoku.com\/blog\/wp-content\/uploads\/2025\/12\/Group-7518.png\" alt=\"Result after applying the last remaining number technique\" class=\"wp-image-415\" style=\"object-fit:cover;width:349px;height:auto\" srcset=\"https:\/\/thesudoku.com\/blog\/wp-content\/uploads\/2025\/12\/Group-7518.png 697w, https:\/\/thesudoku.com\/blog\/wp-content\/uploads\/2025\/12\/Group-7518-300x300.png 300w, https:\/\/thesudoku.com\/blog\/wp-content\/uploads\/2025\/12\/Group-7518-150x150.png 150w\" sizes=\"auto, (max-width: 697px) 100vw, 697px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" style=\"margin-top:var(--wp--preset--spacing--40);margin-bottom:var(--wp--preset--spacing--20)\"\/>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Why You Need to Master the Last Remaining Number<\/h2>\n\n\n\n<p>Spotting Last Remaining Numbers is the bread and butter of Sudoku solving. As puzzles move from Easy to Medium and Hard, you won&#8217;t always find obvious nearly-completed rows. Instead, you will need to rely on this cross-scanning technique to find hidden opportunities and break through complex gridlocks.<\/p>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" style=\"margin-top:var(--wp--preset--spacing--40);margin-bottom:var(--wp--preset--spacing--20)\"\/>\n\n\n\n<div class=\"wp-block-group alignwide is-content-justification-space-between is-nowrap is-layout-flex wp-container-core-group-is-layout-7f2ee5f7 wp-block-group-is-layout-flex\" style=\"padding-top:0;padding-right:var(--wp--preset--spacing--60);padding-bottom:var(--wp--preset--spacing--60);padding-left:var(--wp--preset--spacing--60)\">\n<p style=\"font-size:clamp(14px, 0.875rem + ((1vw - 3.2px) * 0.392), 18px);font-style:normal;font-weight:600\"><a href=\"https:\/\/thesudoku.com\/blog\/last-free-cell\/\" data-type=\"page\" data-id=\"161\">&lt; Last Free Cell<\/a><\/p>\n\n\n\n<p style=\"font-size:clamp(14px, 0.875rem + ((1vw - 3.2px) * 0.392), 18px);font-style:normal;font-weight:600\"><a href=\"https:\/\/thesudoku.com\/blog\/last-possible-cell\/\" data-type=\"page\" data-id=\"431\">Last Possible Cell&gt;<\/a><\/p>\n<\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>&lt; Back How to Find the Last Remaining Number The Last Remaining Number strategy\u2014widely known in the Sudoku community as a Sole Candidate\u2014is a powerful and essential technique for solving puzzles. While the Last Free Cell strategy focuses on scanning a single nearly complete row, column, or block, this technique requires a broader view. You [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page-no-title","meta":{"footnotes":""},"categories":[112],"tags":[],"class_list":["post-409","page","type-page","status-publish","hentry","category-easy-techniques"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Last Remaining Number - TheSudoku.com<\/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:\/\/thesudoku.com\/blog\/last-remaining-number\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Last Remaining Number - TheSudoku.com\" \/>\n<meta property=\"og:description\" content=\"&lt; Back How to Find the Last Remaining Number The Last Remaining Number strategy\u2014widely known in the Sudoku community as a Sole Candidate\u2014is a powerful and essential technique for solving puzzles. 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