{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:08Z","timestamp":1753893788055,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In the game $G_{0}$ two players alternate removing positive numbers of counters from a single pile and the winner is the player who removes the last counter. On the first move of the game, the player moving first can remove a maximum of $k$ counters, $k$ being specified in advance. On each subsequent move, a player can remove a maximum of $f(n,t) $ counters where $t$ was the number of counters removed by his opponent on the preceding move and $n$ is the preceding pile size, where $f:N\\times N\\rightarrow N$ is an arbitrary function satisfying the condition (1): $\\exists t\\in N$ such that for all $n,x\\in N$, $f(n,x) =f(n+t,x) $.  This note extends our earlier paper [E-JC, Vol 10, 2003, N7]. We first solve the game for functions $f:N\\times N\\rightarrow N$ that also satisfy the condition (2): $\\forall n,x\\in N$, $f(n,x+1) -f(n,x) \\geq -1$. Then we state the solution when $f:N\\times N\\rightarrow N$ is restricted only by condition (1) and point out that the more general proof is almost the same as the simpler proof. The solutions when $t\\geq 2$ use multiple bases.<\/jats:p>","DOI":"10.37236\/1145","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:03:00Z","timestamp":1578700980000},"source":"Crossref","is-referenced-by-count":0,"title":["Dynamic Single-Pile Nim Using Multiple Bases"],"prefix":"10.37236","volume":"13","author":[{"given":"Arthur","family":"Holshouser","sequence":"first","affiliation":[]},{"given":"Harold","family":"Reiter","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,3,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1n7\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1n7\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:17:47Z","timestamp":1579303067000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1n7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,3,30]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1145","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2006,3,30]]},"article-number":"N7"}}