{
  "id": "0710.3632",
  "version": "v3",
  "published": "2007-10-19T05:35:06.000Z",
  "updated": "2009-06-02T10:19:35.000Z",
  "title": "2-pile Nim with a Restricted Number of Move-size Imitations",
  "authors": [
    "Urban Larsson"
  ],
  "comment": "18 pages, with an appendix by Peter Hegarty",
  "categories": [
    "math.CO"
  ],
  "abstract": "We study a variation of the combinatorial game of 2-pile Nim. Move as in 2-pile Nim but with the following constraint: Suppose the previous player has just removed say $x>0$ tokens from the shorter pile (either pile in case they have the same height). If the next player now removes $x$ tokens from the larger pile, then he imitates his opponent. For a predetermined natural number $p$, by the rules of the game, neither player is allowed to imitate his opponent on more than $p-1$ consecutive moves. We prove that the strategy of this game resembles closely that of a variant of Wythoff Nim--a variant with a blocking manoeuvre on $p-1$ diagonal positions. In fact, we show a slightly more general result in which we have relaxed the notion of what an imitation is.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-06-02T10:19:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "91A46"
    ],
    "keywords": [
      "restricted number",
      "move-size imitations",
      "wythoff nim-a variant",
      "predetermined natural number",
      "combinatorial game"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.3632L"
    }
  }
}