{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:06Z","timestamp":1753893786155,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We give a non-enumerative proof that the $P$-positions of the hexad game give the Steiner system $S(5,6,12)$. We show that the distributions of nim sums and Welter values of these $P$-positions have simple and surprising regularities.<\/jats:p>","DOI":"10.37236\/1610","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:24:22Z","timestamp":1578709462000},"source":"Crossref","is-referenced-by-count":1,"title":["The Hexad Game"],"prefix":"10.37236","volume":"8","author":[{"given":"Joseph","family":"Kahane","sequence":"first","affiliation":[]},{"given":"Alexander J.","family":"Ryba","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2000,5,18]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i2r11\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i2r11\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:23:16Z","timestamp":1579324996000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v8i2r11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,5,18]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2001,2,6]]}},"URL":"https:\/\/doi.org\/10.37236\/1610","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2000,5,18]]},"article-number":"R11"}}