http://swrc.ontoware.org/ontology#TechnicalReport
A Generalized Ryuoh-Nim:A Variant of the classical game of Wythoff Nim
en
パズルゲームの理論
Kwansei Gakuin High School
Hyogo University of Teacher Education
Kwansei Gakuin High School
Kwansei Gakuin High School
Ryohei Miyadera
Masanori Fukui
Yushi Nakaya
Yuki Tokuni
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.
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-41
14
1-3
2016-07-29
2188-8914