{"id":34721,"date":"2025-12-22T00:00:43","date_gmt":"2025-12-22T08:00:43","guid":{"rendered":"https:\/\/www.gmpuzzles.com\/blog\/?p=34721"},"modified":"2025-12-25T14:38:08","modified_gmt":"2025-12-25T22:38:08","slug":"ratio-pairs-thermo-sudoku-by-clover","status":"publish","type":"post","link":"https:\/\/www.gmpuzzles.com\/blog\/2025\/12\/ratio-pairs-thermo-sudoku-by-clover\/","title":{"rendered":"Ratio Pairs Thermo-Sudoku by clover!"},"content":{"rendered":"<p>(This post is part of the <a href=\"https:\/\/www.gmpuzzles.com\/blog\/tag\/gas\/\">Genuinely Approachable Sudoku (GAS)<\/a> series.)<br \/>\n<em>The recent and remarkable set of paired variations by clover! continues with some thermometer shapes and some black dots indicating doubled values.<\/em><\/p>\n<p align=\"center\"><img decoding=\"async\" src=\"https:\/\/www.gmpuzzles.com\/images\/puzzles2025\/251222-RatioPairsThermoSudoku-PolkaDots.png\" alt=\"Ratio Pairs Thermo-Sudoku by clover!\" \/><\/p>\n<p align=\"center\"><a href=\"https:\/\/www.gmpuzzles.com\/images\/puzzles2025\/251222-RatioPairsThermoSudoku-PolkaDots.pdf\">PDF<\/a><\/p>\n<p>or <a href=\"https:\/\/gmpuzzles.com\/s\/251222Polk\">solve online<\/a> (using SudokuPad)<\/p>\n<p><b>Theme:<\/b> Polka Dots<\/p>\n<p><b>Author\/Opus:<\/b> This is the 88th puzzle from Clover, part of the Genuinely Approachable Sudoku (<a href=\"https:\/\/sudokutheory.com\/gas\/\">GAS<\/a>) team.<\/p>\n<p><b>Rules:<\/b> Standard Sudoku rules (insert a number from 1 to 9 into each cell so that no number repeats in any row, column, or bold region). If a black circle is given between two adjacent cells, then the two numbers must have a ratio of 2. Pairs of cells without circles can have any relationship. Also, some thermometer shapes are in the grid; numbers must be strictly increasing from the round bulb to the flat end.<\/p>\n<p><b>GAS Time Standards (highlight to view):<\/b> Two party hats (\ud83c\udfa9\ud83e\udd73): <span style=\"color: white;background-color: white\">7:00<\/span>; One party hat (\ud83e\udd73): <span style=\"color: white;background-color: white\">13:00<\/span>. All other solvers earn a \ud83e\udd95: <span style=\"color: white;background-color: white\">dotty Dollodon<\/span>.<\/p>\n<p><b>Thomas Hits the GAS (highlight to view):<\/b> <span style=\"color: white;background-color: white\">3:10<\/span>, with <a href=\"https:\/\/www.gmpuzzles.com\/images\/puzzles2025\/sudokupad-clover-Dec_19_2025_Polka_Dots-a801-d191.replay\">SudokuPad replay file<\/a> shared as a download for now (requires loading via settings menu with improvements expected before people should use this regularly).<\/p>\n<p><b>Solution:<\/b> <a href=\"https:\/\/www.gmpuzzles.com\/images\/puzzles2025\/251222-RatioPairsThermoSudoku-PolkaDots-soln.pdf\">PDF<\/a> and <a href=\"https:\/\/youtu.be\/mY1xXQ1TW50\">solving video<\/a> with explanation from GAS team.<\/p>\n<p><b>Note:<\/b> Follow this link for other less common variations of <a href=\"https:\/\/www.gmpuzzles.com\/blog\/tag\/sudoku-3+variation-2\/\">Sudoku<\/a>.<\/p>\n<p><b>Note 2:<\/b>\u00a0Comments on the blog are great! For a more interactive discussion, please also consider using our\u00a0<a href=\"https:\/\/discord.com\/channels\/1059513302847336469\/1380897111599616020\">Daily GAS discussion<\/a>\u00a0post\u00a0on the GMPuzzles Discord. Not a member of the Discord? Click\u00a0<a href=\"https:\/\/discord.gg\/RNNfEBEbQS\">this link<\/a>\u00a0for basic access.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>(This post is part of the Genuinely Approachable Sudoku (GAS) series.) The recent and remarkable set of paired variations by clover! continues with some thermometer shapes and some black dots indicating doubled values. PDF or solve online (using SudokuPad) Theme: Polka Dots Author\/Opus: This is the 88th puzzle from Clover, part of the Genuinely Approachable [&hellip;]<\/p>\n","protected":false},"author":444,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,126],"tags":[8,15,56,237],"class_list":["post-34721","post","type-post","status-publish","format-standard","hentry","category-puzzle","category-othersudoku","tag-sudoku-3","tag-wednesdaythursday","tag-variation-2","tag-gas"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Ratio Pairs Thermo-Sudoku by clover! - The Art of Puzzles<\/title>\n<meta name=\"description\" content=\"The recent and remarkable set of paired variations by clover! continues with some thermometer shapes and black dots indicating doubling.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.gmpuzzles.com\/blog\/2025\/12\/ratio-pairs-thermo-sudoku-by-clover\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Ratio Pairs Thermo-Sudoku by clover! - The Art of Puzzles\" \/>\n<meta property=\"og:description\" content=\"The recent and remarkable set of paired variations by clover! continues with some thermometer shapes and black dots indicating doubling.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.gmpuzzles.com\/blog\/2025\/12\/ratio-pairs-thermo-sudoku-by-clover\/\" \/>\n<meta property=\"og:site_name\" content=\"The Art of Puzzles\" \/>\n<meta property=\"article:published_time\" content=\"2025-12-22T08:00:43+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-12-25T22:38:08+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.gmpuzzles.com\/images\/puzzles2025\/251222-RatioPairsThermoSudoku-PolkaDots.png\" \/>\n<meta name=\"author\" content=\"Clover\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@drsudoku\" \/>\n<meta name=\"twitter:site\" content=\"@drsudoku\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Clover\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/www.gmpuzzles.com\\\/blog\\\/2025\\\/12\\\/ratio-pairs-thermo-sudoku-by-clover\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.gmpuzzles.com\\\/blog\\\/2025\\\/12\\\/ratio-pairs-thermo-sudoku-by-clover\\\/\"},\"author\":{\"name\":\"Clover\",\"@id\":\"https:\\\/\\\/www.gmpuzzles.com\\\/blog\\\/#\\\/schema\\\/person\\\/18e8374ccaf31b1bfa1dc36c28c5c56d\"},\"headline\":\"Ratio Pairs Thermo-Sudoku by clover!\",\"datePublished\":\"2025-12-22T08:00:43+00:00\",\"dateModified\":\"2025-12-25T22:38:08+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/www.gmpuzzles.com\\\/blog\\\/2025\\\/12\\\/ratio-pairs-thermo-sudoku-by-clover\\\/\"},\"wordCount\":245,\"commentCount\":0,\"image\":{\"@id\":\"https:\\\/\\\/www.gmpuzzles.com\\\/blog\\\/2025\\\/12\\\/ratio-pairs-thermo-sudoku-by-clover\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/www.gmpuzzles.com\\\/images\\\/puzzles2025\\\/251222-RatioPairsThermoSudoku-PolkaDots.png\",\"keywords\":[\"sudoku\",\"wed\\\/thurs\",\"variation\",\"gas\"],\"articleSection\":[\"Puzzle\",\"Other Sudoku\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/www.gmpuzzles.com\\\/blog\\\/2025\\\/12\\\/ratio-pairs-thermo-sudoku-by-clover\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/www.gmpuzzles.com\\\/blog\\\/2025\\\/12\\\/ratio-pairs-thermo-sudoku-by-clover\\\/\",\"url\":\"https:\\\/\\\/www.gmpuzzles.com\\\/blog\\\/2025\\\/12\\\/ratio-pairs-thermo-sudoku-by-clover\\\/\",\"name\":\"Ratio Pairs Thermo-Sudoku by clover! 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