2021-08-02T15:03:48Zhttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_oaipmhoai:ipsj.ixsq.nii.ac.jp:001717822020-04-01T00:33:29Z01164:05336:08617:08867
A Generalized Ryuoh-Nim:A Variant of the classical game of Wythoff NimA Generalized Ryuoh-Nim:A Variant of the classical game of Wythoff Nimengパズルゲームの理論http://id.nii.ac.jp/1001/00171748/Technical Reporthttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_action_common_download&item_id=171782&item_no=1&attribute_id=1&file_no=1Copyright (c) 2016 by the Information Processing Society of JapanKwansei Gakuin High SchoolHyogo University of Teacher EducationKwansei Gakuin High SchoolKwansei Gakuin High SchoolRyohei, MiyaderaMasanori, FukuiYushi, NakayaYuki, TokuniWe introduce the impartial game of Ryuo Nim, a variant of the classical game of Wythoff Nim. In the latter game, two players take turns in moving a single Queen of Chess on a large board, attempting to be the first to put her in the lower left corner, position (0,0). Instead of the queen used in Wythoff Nim, we use the Ryuo that is a promoted Hisha (rook) piece of Japanese chess. The Ryuo combines the power of the rook and king in western chess. We prove that the Grundy number for this variant is expressed by G((x, y)) = mod(x +y, 3)+3(x/3 y/3), where mod(x +y, 3) is the remaider of x+y when divided by 3. We study a generalization of the Ryuo Nim whose Grudy number is expressed by mod(x + y, p) + p(x/py/p) for a natural number p. We also study a generalized Ryuo Nim with a pass.We introduce the impartial game of Ryuo Nim, a variant of the classical game of Wythoff Nim. In the latter game, two players take turns in moving a single Queen of Chess on a large board, attempting to be the first to put her in the lower left corner, position (0,0). Instead of the queen used in Wythoff Nim, we use the Ryuo that is a promoted Hisha (rook) piece of Japanese chess. The Ryuo combines the power of the rook and king in western chess. We prove that the Grundy number for this variant is expressed by G((x, y)) = mod(x +y, 3)+3(x/3 y/3), where mod(x +y, 3) is the remaider of x+y when divided by 3. We study a generalization of the Ryuo Nim whose Grudy number is expressed by mod(x + y, p) + p(x/py/p) for a natural number p. We also study a generalized Ryuo Nim with a pass.AA12049625研究報告エンタテインメントコンピューティング（EC）2016-EC-4114132016-07-292188-89142016-07-25