{"id":2115004,"date":"2026-08-27T15:15:27","date_gmt":"2026-08-27T12:15:27","guid":{"rendered":"https:\/\/analyse.optim.biz\/?p=2115004"},"modified":"2026-08-27T15:15:27","modified_gmt":"2026-08-27T12:15:27","slug":"this-brain-teaser-lied-to-players-for-3-years-and-math-finally-caught-it","status":"publish","type":"post","link":"https:\/\/analyse.optim.biz\/?p=2115004","title":{"rendered":"This Brain Teaser Lied to Players for 3 Years, and Math Finally Caught It"},"content":{"rendered":"

[analyse_image type=”featured” src=”https:\/\/gizmodo.com\/app\/uploads\/2026\/08\/Digit-Party-1200×675.jpg”]<\/p>\n

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Digit Party, an online brain teaser, has attracted hundreds of thousands of math lovers since its launch three years ago. But the creators of the game\u2014two mathematicians\u2014now have a confession to make. Your high scores were probably fake.<\/p>\n

In a recent paper published in Math Horizons, mathematicians Robert Brignall and Vincent Vatter, of The Open University in the U.K. and the University of Florida, respectively, admitted that they did not know how to calculate the true high scores. They\u2019re coming clean as they\u2019ve now solved the issue, specifically by precomputing the true \u201cperfect score\u201d for every possible game. Technically, the average error was small, at about 2 points, with the maximum being 6 points off, and the game \u201clied\u201d 55 times out of the past 1,096 puzzles. At the same time, this \u201clie\u201d demonstrates a surprisingly common problem in practical mathematics, namely optimization hurdles also present in scheduling, logistics, and manufacturing.<\/p>\n

\u201cWe knew there was this issue, but we didn\u2019t know how to fix it,\u201d Vatter said in a statement. \u201cWe had a number we knew nobody could beat. Most of the time it was actually reachable, but about 5% of the time it wasn\u2019t, and we had no way to tell the difference. We knew it this whole time, and it bugged us.\u201d<\/p>\n

How to play<\/h2>\n
\"Digit
A screenshot of my daily shot at Digit Party. The percent score represents my performance against a \u201cperfect\u201d score. Credit: Digit Party\/Robert Brignall\/Vincent Vatter<\/figcaption><\/figure>\n

Digit Party\u2019s formula is simple and oddly addicting. The goal is to arrange 25 digits from 1 to 9 on a 5-by-5 grid. You get one number and a preview of the next number. You can place a number anywhere you\u2019d like, but to score points, you have to place the same number next to each other (horizontally, vertically, or diagonally), and you score points equal to that digit\u2019s value. According to the paper, the game displays your score as a percentage of a theoretical maximum\u2014that is, a perfect score that assumes the player sees \u201call 25 digits in advance and place them with perfect foresight.\u201d<\/p>\n

\u201cAt least, that\u2019s what we claimed,\u201d the pair wrote in the paper. \u201cWe have been lying to players for three years. In our defense, it wasn\u2019t on purpose.\u201d<\/p>\n

In truth, the \u201cmaximum score\u201d was an approximation based on an upper bound. It didn\u2019t properly represent the optimal arrangement of each group of equal digits. To be fair, the error margins weren\u2019t huge. For instance, if one day\u2019s true maximum was 186, the approximation would calculate players\u2019 percentages based on an upper bound of 192.<\/p>\n

Finding the true maximum<\/h2>\n

In the statement, Vatter likened the issue to packing a suitcase. You might start by figuring out how best to arrange your shirts, then your suits. But sometimes, you just have too many clothes, and \u201csomething has to get crumpled,\u201d he explained. The so-called \u201coptimization\u201d question then concerns the \u201csmartest thing to sacrifice,\u201d or \u201ccrumple,\u201d for any combination of packing lists.<\/p>\n

\"Pareto
An example of two different Pareto-optimal tilings for an identical set of numbers given by the game. The scores for each arrangement are 185 (left) and 186 (right). \u00a9 Vatter et al., 2026<\/figcaption><\/figure>\n

Solving this issue for Digit Party wasn\u2019t easy. The pair could technically \u201cship an integer programming solver to every player\u201d or cram in some extra code that might make the game \u201cmelt your phone.\u201d Clearly, that\u2019s not ideal. And so, the mathematicians decided to \u201cprecompute the true maxima for every possible board and encode the answers in the code.\u201d<\/p>\n

That added up a dizzying number of possibilities\u201413.9 million different sets of digits\u2014which dropped to 1,291 once the mathematicians grouped the results according to shared patterns of repeated numbers. And within those 1,291, 891 outcomes didn\u2019t require any trade-offs. For the remaining 400, the pair manually computed the highest possible score; for example, if a player can\u2019t fit all 4s and 8s, it\u2019d be smarter to drop 4, as matching 8s would give you a higher score.<\/p>\n

Having said that, the team finished its confession with another admission: What\u2019s the best strategy? We don\u2019t actually know.<\/p>\n

\u201cWe still have no idea how to play,\u201d Vatter said. \u201cRobert and I play quite differently, and nobody knows who\u2019s better.\u201d<\/p>\n<\/div>\n<\/article>\n

\n

Digit Party, an online brain teaser, has attracted hundreds of thousands of math lovers since its launch three years ago. But the creators of the game\u2014two mathematicians\u2014now have a confession to make. Your high scores were probably fake.<\/p>\n

In a recent paper published in Math Horizons, mathematicians Robert Brignall and Vincent Vatter, of The Open University in the U.K. and the University of Florida, respectively, admitted that they did not know how to calculate the true high scores. They\u2019re coming clean as they\u2019ve now solved the issue, specifically by precomputing the true \u201cperfect score\u201d for every possible game. Technically, the average error was small, at about 2 points, with the maximum being 6 points off, and the game \u201clied\u201d 55 times out of the past 1,096 puzzles. At the same time, this \u201clie\u201d demonstrates a surprisingly common problem in practical mathematics, namely optimization hurdles also present in scheduling, logistics, and manufacturing.<\/p>\n

\u201cWe knew there was this issue, but we didn\u2019t know how to fix it,\u201d Vatter said in a statement. \u201cWe had a number we knew nobody could beat. Most of the time it was actually reachable, but about 5% of the time it wasn\u2019t, and we had no way to tell the difference. We knew it this whole time, and it bugged us.\u201d<\/p>\n

How to play<\/h2>\n
\"Digit
A screenshot of my daily shot at Digit Party. The percent score represents my performance against a \u201cperfect\u201d score. Credit: Digit Party\/Robert Brignall\/Vincent Vatter<\/figcaption><\/figure>\n

Digit Party\u2019s formula is simple and oddly addicting. The goal is to arrange 25 digits from 1 to 9 on a 5-by-5 grid. You get one number and a preview of the next number. You can place a number anywhere you\u2019d like, but to score points, you have to place the same number next to each other (horizontally, vertically, or diagonally), and you score points equal to that digit\u2019s value. According to the paper, the game displays your score as a percentage of a theoretical maximum\u2014that is, a perfect score that assumes the player sees \u201call 25 digits in advance and place them with perfect foresight.\u201d<\/p>\n

\u201cAt least, that\u2019s what we claimed,\u201d the pair wrote in the paper. \u201cWe have been lying to players for three years. In our defense, it wasn\u2019t on purpose.\u201d<\/p>\n

In truth, the \u201cmaximum score\u201d was an approximation based on an upper bound. It didn\u2019t properly represent the optimal arrangement of each group of equal digits. To be fair, the error margins weren\u2019t huge. For instance, if one day\u2019s true maximum was 186, the approximation would calculate players\u2019 percentages based on an upper bound of 192.<\/p>\n

Finding the true maximum<\/h2>\n

In the statement, Vatter likened the issue to packing a suitcase. You might start by figuring out how best to arrange your shirts, then your suits. But sometimes, you just have too many clothes, and \u201csomething has to get crumpled,\u201d he explained. The so-called \u201coptimization\u201d question then concerns the \u201csmartest thing to sacrifice,\u201d or \u201ccrumple,\u201d for any combination of packing lists.<\/p>\n

\"Pareto
An example of two different Pareto-optimal tilings for an identical set of numbers given by the game. The scores for each arrangement are 185 (left) and 186 (right). \u00a9 Vatter et al., 2026<\/figcaption><\/figure>\n

Solving this issue for Digit Party wasn\u2019t easy. The pair could technically \u201cship an integer programming solver to every player\u201d or cram in some extra code that might make the game \u201cmelt your phone.\u201d Clearly, that\u2019s not ideal. And so, the mathematicians decided to \u201cprecompute the true maxima for every possible board and encode the answers in the code.\u201d<\/p>\n

That added up a dizzying number of possibilities\u201413.9 million different sets of digits\u2014which dropped to 1,291 once the mathematicians grouped the results according to shared patterns of repeated numbers. And within those 1,291, 891 outcomes didn\u2019t require any trade-offs. For the remaining 400, the pair manually computed the highest possible score; for example, if a player can\u2019t fit all 4s and 8s, it\u2019d be smarter to drop 4, as matching 8s would give you a higher score.<\/p>\n

Having said that, the team finished its confession with another admission: What\u2019s the best strategy? We don\u2019t actually know.<\/p>\n

\u201cWe still have no idea how to play,\u201d Vatter said. \u201cRobert and I play quite differently, and nobody knows who\u2019s better.\u201d<\/p>\n<\/div>\n

[analyse_source url=”https:\/\/gizmodo.com\/this-brain-teaser-lied-to-players-for-3-years-and-math-finally-caught-it-2000803833″]<\/p>\n","protected":false},"excerpt":{"rendered":"

[analyse_image type=”featured” src=”https:\/\/gizmodo.com\/app\/uploads\/2026\/08\/Digit-Party-1200×675.jpg”] Digit Party, an online brain teaser, has attracted hundreds of thousands of math lovers since its launch three years ago. But the creators of the game\u2014two mathematicians\u2014now have a confession to make. Your high scores were probably fake. In a recent paper published in Math Horizons, mathematicians Robert Brignall and Vincent Vatter, […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[226,53],"class_list":["post-2115004","post","type-post","status-publish","format-standard","hentry","category-politics","tag-crawlmanager","tag-gizmodo-com"],"_links":{"self":[{"href":"https:\/\/analyse.optim.biz\/index.php?rest_route=\/wp\/v2\/posts\/2115004","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/analyse.optim.biz\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/analyse.optim.biz\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/analyse.optim.biz\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/analyse.optim.biz\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2115004"}],"version-history":[{"count":0,"href":"https:\/\/analyse.optim.biz\/index.php?rest_route=\/wp\/v2\/posts\/2115004\/revisions"}],"wp:attachment":[{"href":"https:\/\/analyse.optim.biz\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2115004"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/analyse.optim.biz\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2115004"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/analyse.optim.biz\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2115004"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}