{"id":"https://openalex.org/W4236288184","doi":"https://doi.org/10.1145/2578281","title":"Puzzled: Solutions and sources","display_name":"Puzzled: Solutions and sources","publication_year":2014,"publication_date":"2014-02-26","ids":{"openalex":"https://openalex.org/W4236288184","doi":"https://doi.org/10.1145/2578281"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1145/2578281","pdf_url":null,"source":{"id":"https://openalex.org/S103482838","display_name":"Communications of the ACM","issn_l":"0001-0782","issn":["0001-0782","1557-7317"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056680757","display_name":"Peter Winkler","orcid":"https://orcid.org/0000-0002-1259-3574"},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"funder","lineage":["https://openalex.org/I107672454"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Peter Winkler","raw_affiliation_strings":["Dartmouth College, Hanover, NH"],"affiliations":[{"raw_affiliation_string":"Dartmouth College, Hanover, NH","institution_ids":["https://openalex.org/I107672454"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5056680757"],"corresponding_institution_ids":["https://openalex.org/I107672454"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":0,"max":66},"biblio":{"volume":"57","issue":"3","first_page":"109","last_page":"109"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11574","display_name":"Artificial Intelligence in Games","score":0.9897,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11574","display_name":"Artificial Intelligence in Games","score":0.9897,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/liberian-dollar","display_name":"Liberian dollar","score":0.60078824},{"id":"https://openalex.org/keywords/lottery","display_name":"Lottery","score":0.5009446}],"concepts":[{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.6822778},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.67130834},{"id":"https://openalex.org/C109168655","wikidata":"https://www.wikidata.org/wiki/Q242988","display_name":"Liberian dollar","level":2,"score":0.60078824},{"id":"https://openalex.org/C2777340749","wikidata":"https://www.wikidata.org/wiki/Q6684955","display_name":"Lottery","level":2,"score":0.5009446},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41731602},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39156953},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34820193},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.18776965},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10115054},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.082300425}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1145/2578281","pdf_url":null,"source":{"id":"https://openalex.org/S103482838","display_name":"Communications of the ACM","issn_l":"0001-0782","issn":["0001-0782","1557-7317"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4303183270","https://openalex.org/W4236288184","https://openalex.org/W3125197004","https://openalex.org/W3095881110","https://openalex.org/W2955320052","https://openalex.org/W2921671016","https://openalex.org/W2803931294","https://openalex.org/W2364124353","https://openalex.org/W2108243443","https://openalex.org/W1830847883"],"abstract_inverted_index":{"Last":[0],"month":[1],"(February":[2],"2014)":[3],"we":[4,34],"posted":[5],"three":[6],"games":[7],"in":[8,20,124,144,160,250,385,456,467,490,492],"which":[9,125,247],"you":[10,28,42,290,311,326,343,347],"were":[11],"asked":[12],"to":[13,37,79,85,183,211,401],"pick":[14],"a":[15,54,63,204,215,221,303,308,367,380,387,418,446,460,481,483],"positive":[16,280,283],"integer.":[17],"The":[18,162,177,228,425,472,498],"question":[19],"each":[21,95,502],"was:":[22],"What":[23],"is":[24,75,119,208,214,236,286,307,365,379,414,451],"the":[25,60,70,83,105,108,114,127,130,137,225,269,273,299,313,333,337,354,356,374,377,398,415,442,495,506,512],"highest":[26,229,309,513],"number":[27,59,110,132,230,310,321,399,447,474,499,509],"should":[29,233,291,316],"think":[30],"about":[31,435],"picking?":[32],"Here,":[33,104],"offer":[35],"solutions":[36],"all":[38,350],"three.":[39],"How":[40],"did":[41,201],"do?":[43],"1.":[44],"Found":[45],"dollar":[46,84],".":[47,103,244,323],"Alice":[48],"and":[49,62,82,168,197,395,422,432,439],"Bob":[50],"are":[51,434],"vying":[52],"for":[53,67,76,277,298,392,397,427,485],"found":[55],"dollar,":[56],"with":[57,129,191,220,282,404],"lowest":[58,507],"winner":[61],"tie":[64,141],"winning":[65,473,508],"it":[66,118,207,320],"neither.":[68],"Sadly,":[69],"only":[71,122,226],"\"Nash":[72],"equilibrium\"":[73],"solution":[74,180],"both":[77,360],"players":[78,335,359,501],"choose":[80,336],"\"1\"":[81],"go":[86],"unclaimed---a":[87],"mini":[88],"\"prisoner's":[89],"dilemma.\"":[90],"Collaboration":[91],"could":[92],"have":[93],"won":[94],"of":[96,107,165,301,417,444,500],"them":[97],"50":[98],"cents.":[99],"2.":[100],"Zero":[101],"sum":[102],"writer":[106],"lower":[109,120,339],"wins":[111],"$1":[112],"from":[113,136],"other":[115,138,314,334,357],"player,":[116],"unless":[117],"by":[121,153],"1,":[123,429],"case":[126],"player":[128,232],"higher":[131],"would":[133,142,181,325,348],"win":[134,327,349],"$2":[135],"player.":[139],"A":[140,255,477],"result":[143],"no":[145,287],"money":[146],"changing":[147],"hands.":[148],"This":[149,245],"problem":[150],"was":[151,475,510],"published":[152],"Martin":[154],"Gardner,":[155],"appearing":[156],"as":[157,265],"Problem":[158],"11.13":[159],"his":[161],"Collossal":[163],"Book":[164],"Short":[166],"Puzzles":[167],"Problems":[169],"(W.W.":[170],"Norton":[171],"&":[172],"Co.,":[173],"New":[174],"York,":[175],"2006).":[176],"Nash":[178,216,381,389],"equilibrium":[179,217,274,390],"be":[182,402],"write":[184],"\"1,\"":[185],"\"2,\"":[186],"\"3,\"":[187],"\"4,\"":[188],"or":[189],"\"5\"":[190],"probabilities":[192,426],"1/16,":[193,198],"5/16,":[194,196],"1/4,":[195],"respectively.":[199],"(Gardner":[200],"not":[202,209],"provide":[203],"proof,":[205],"but":[206],"difficult":[210],"show":[212],"this":[213],"strategy":[218,275,378,391],"and,":[219],"little":[222],"more":[223],"work,":[224],"one.)":[227],"either":[231],"consider":[234,292],"writing":[235],"thus":[237,366],"\"5.\"<!--":[238],"END_PAGE_1":[239],"-->":[240],"3.":[241],"Swedish":[242,461],"lottery":[243],"game,":[246],"I":[248,458],"included":[249],"my":[251],"book":[252],"Mathematical":[253],"Puzzles:":[254],"Conoisseur's":[256],"Collection":[257],"(A":[258],"K":[259],"Peters":[260],"Ltd.,":[261],"Natick,":[262],"MA,":[263],"2001)":[264],"\"Swedish":[266],"Lottery,\"":[267],"has":[268],"surprising":[270],"property":[271],"that":[272,305,376],"calls":[276],"playing":[278,328],"every":[279],"integer":[281,289],"probability.":[284],"There":[285,383],"largest":[288],"playing.":[293],"To":[294],"see":[295,517],"this,":[296],"imagine":[297],"sake":[300],"reaching":[302],"contradiction":[304],"there":[306],"(and":[312],"players)":[315],"ever":[317],"play;":[318],"call":[319],"k":[322,329,345,363,371],"When":[324],"?":[330],"Only":[331],"when":[332],"same":[338],"number.":[340],"But":[341],"if":[342],"played":[344],"+1,":[346],"those":[351],"times":[352,355],"plus":[353],"two":[358],"play":[361],"k.":[362],"+1":[364],"better":[368],"choice":[369],"than":[370,449],",":[372],"contradicting":[373],"assumption":[375],"equilibrium.":[382],"is,":[384],"fact,":[386],"common":[388],"Alice,":[393],"Bob,":[394],"Charlie---calling":[396],"j":[400,410],"selected":[403],"probability":[405,443],"(1--":[406],"r":[407,409,413],")":[408],"\u22121":[411],"where":[412],"root":[416],"certain":[419],"cubic":[420],"equation":[421],"approximately":[423],"0.543689.":[424],"choosing":[428,445],"2,":[430],"3,":[431],"4":[433],"0.456311,":[436],"0.248091,":[437],"0.134884,":[438],"0.073335,":[440],"respectively;":[441],"greater":[448],"100":[450],"teeny.":[452],"As":[453],"an":[454],"experiment":[455],"2010,":[457],"ran":[459],"Lottery":[462],"among":[463],"40":[464],"graduate":[465],"students":[466],"Dartmouth's":[468],"Computer":[469],"Science":[470],"Department.":[471],"6.":[476],"much":[478],"larger":[479],"version---actually":[480],"game":[482],"day":[484,503],"47":[486],"straight":[487],"days---was":[488],"run":[489],"Sweden":[491],"2007":[493],"under":[494],"name":[496],"\"Limbo.\"":[497],"averaged":[504],"53,785;":[505],"162,":[511],"4,465.":[514],"For":[515],"more,":[516],"http://swopec.hhs.se/hastef/papers/hastef0671.pdf.":[518]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W4236288184","counts_by_year":[],"updated_date":"2025-01-25T13:03:33.189814","created_date":"2022-05-12"}