[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-503229-105":59,"doc-detail-503229-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","em-and-the-foundations-of-ai-a-classic-intelligence-test-mensa-problem-50","EM and the Foundations of AI - A Classic Intelligence Test - Mensa Problem #50","","A Mensa-style intelligence test problem analyzes a contrived darts scenario to illustrate a logicist view of intelligence. It shows how factorisations of 72 into three factors can be disambiguated by the sum, once the solver learns an eldest daughter named Vanessa. The text then critiques logicism’s assumptions about abstract inference, psychological realism, embodiment, indexicality, and the imagination needed to connect abstract models with real-world premises. It discusses limits and potential relevance to inference engines and empirical modelling.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/em-and-the-foundations-of-ai-a-classic-intelligence-test-mensa-problem-50/503229/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/em-and-the-foundations-of-ai-a-classic-intelligence-test-mensa-problem-50/503229.png","ImageObject",300,407,{"name":92,"@type":93},"Kyle","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-14","2026-10-03",true,{"@type":102,"interactionType":103,"userInteractionCount":8},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How does the puzzle determine the daughters’ ages from the clue and score?","Question",{"text":112,"@type":113},"The ages correspond to factorisations of 72 into three factors. Fred’s uncertainty is resolved once he knows there is an eldest daughter, because the relevant pair of factorisations is disambiguated by the sum.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What is the key logical observation about factorisations of 72?",{"text":117,"@type":113},"The puzzle hinges on the fact that 72 can be written as 3*3*8 or 6*6*2, and these two options produce different sums. The observation about the sums allows the solver to eliminate the wrong factorisation.",{"name":119,"@type":110,"acceptedAnswer":120},"Why does the text argue that the problem is a parody of intelligence?",{"text":121,"@type":113},"It claims the scenario depends on an artificially closed world model and assumes rapid, abstract reasoning while ignoring psychological realism and commonsense obstacles, making the “intelligence” test less representative of real cognitive processes.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},503229,1791980983,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":8,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":24},3985741905716,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","An extract from EM paper \\#50: EM and the Foundations of AI A Classic Intelligence Test  \nThe following problem illustrates one popular view of intelligence that has much in common with the logicist perspective as portrayed in Kirsh, 1991. It is drawn from a publication by Mensa, a society whose membership comprises people with a high \"intelligence quotient\" .  \nThe Captain of the darts team needs 72 to win. Before throwing a dart, heremarks that (coincidentally) 72 is the product of the ages of his three daughters. After throwing one dart, he remarks that (coincidentally) the score for the dart he has just thrown is the sum of the ages of his  \ndaughters. Fred, his opponent, observes at this point that he does not know the ages of the Captain's daughters. \"I'll give you a clue\", says the  \nCaptain. My eldest daughter is called Vanessa. \"I see\", says Fred. \"Now I know their ages\".  \nThe solution to this problem centres on the fact that factorisations of 72 into 3 factors are disambiguated by the sum of factors but for the pair of factorisations:  \n72 = 3 * 3 * 8 = 6 * 6 * 2.  \nBy observing that he does not know the ages of the daughters, Fred discloses to the solver that one or other of these factorisations of 72 is the required one. (Note that, to make his observation, Fred does not need to know-as we as solvers do-that no other pair of factorisations of 72 into three yields the same sum, since he knows that the Captain has scored 14.) When he knows there is an eldest daughter, he knows that the ages of the daughters are 3, 3 and 8.  \nThis puzzle illustrates several ingredients of logicism discussed in Kirsh. The problem is contrived around a mathematical model in the poser's mind. The casual and artificial way in which the abstract problem is placed in a real-world context echoes the modularity of'inventing conceptualizations' and 'grounding concepts' presumed in logicism (Kirsh,1991) . Embodiment plays a contrived role in the problem. The issue of psychological realism is not addressed. It is assumed that Fred exercises instantaneous-or at least very rapid-inference skills on-line, whilst \"knowing the ages of the daughters\" is an abstract concept, unconnected with being able to associate an age with a daughter who might turn up at the darts match. Nor is indexicality respected. In order to draw any inferences, a single Mensa-like persona must be imposed on the agents in the puzzle (the Captain and Fred) and on the poser and solver also.  \nThe remarkable thing about problems of this nature is that the IQ-literate reader adopts the conventions of the problem poser so readily. Why should we regard problem-solving of this nature as intelligent? Perhaps because it involves being able to see through the contrived presentation to make ingenious abstract inferences, discounting the commonsense obstacles to deduction (cf. Naur's analysis of logical deduction in Sherlock Holmes stories (Naur,1995): \"truth and logical inference in human affairs is a matter of the way in which these affairs are described\") .  \nTo some degree, facility in making abstractions is a quality of intelligence. Some commonsense facts about the world must be taken for granted to make sense of the problem. For example, a game of darts takes place on such a timescale that the ages of the children are fixed for its duration. 14 is a legitimate score for one dart. Yet the puzzle is posed so artificially that it is almost a parody of intelligence.  \nA complementary mental skill is far less well-represented in logicism. This is the ability to transpose the problem imaginatively so as to disclose the implicit presumptions about the relationship between the abstract and the real-world elements. Imagination of this kind can subvert the intelligence test. A suspension of disbelief is needed in supposing that the Captain and Fred are mathematically adept and sober enough to factorise 72 in their heads whilst simultaneously taking turns at darts, or that Fred determines th","cbCaia2zljI7hMin","https://ap.wps.com/l/cbCaia2zljI7hMin","pdf",31565,"English","# EM and the Foundations of AI - A Classic Intelligence Test\n## Mensa problem setup and solution logic\n## Logicism critique: modelling, inference, and assumptions\n## Implications for inference engines and empirical modelling\n## References","[{\"question\":\"How does the puzzle determine the daughters’ ages from the clue and score?\",\"answer\":\"The ages correspond to factorisations of 72 into three factors. Fred’s uncertainty is resolved once he knows there is an eldest daughter, because the relevant pair of factorisations is disambiguated by the sum.\"},{\"question\":\"What is the key logical observation about factorisations of 72?\",\"answer\":\"The puzzle hinges on the fact that 72 can be written as 3*3*8 or 6*6*2, and these two options produce different sums. The observation about the sums allows the solver to eliminate the wrong factorisation.\"},{\"question\":\"Why does the text argue that the problem is a parody of intelligence?\",\"answer\":\"It claims the scenario depends on an artificially closed world model and assumes rapid, abstract reasoning while ignoring psychological realism and commonsense obstacles, making the “intelligence” test less representative of real cognitive processes.\"}]","EM and the Foundations of AI - A Classic Intelligence Test - Mensa Problem #50 | PDF",1791052290]