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Paper Abstract and Keywords
Presentation 2016-09-06 13:30
Games with a Single Pile of Stones and Number Theoretic Problems
Yoshihiro Tsukamura (SONY), Yoshihide Igarashi, Yuta Urabe, Koichi Yamazaki (Gunma Univ.) COMP2016-17
Abstract (in Japanese) (See Japanese page) 
(in English) The game discussed in this paper is played alternately by two players, removing at least one and at most m stones from the single pile of stones at each turn. Each player is prohibited from taking the same number of stones as the number of stones taken by the opponent at the immediately previous turn. A player who makes the pile empty wins the game. Furthermore, when a player cannot take any number of stones from the non-empty pile due to the prohibition rule, the opponent becomes the winner. This game is denoted by MSP(m). We formulate the initial numbers of stones at the pile such that one player of MSP(m) is promised to become the winner. According to the formula we categorize MSP(m)’s into types 1,2,3,··· ,k,k + 1,···. We give an algorithm for deciding the type number of MSP(m) for any given m. We prove that for any positive integer k, there exists a positive integer m such that the type number of MSP(m) is k.
Keyword (in Japanese) (See Japanese page) 
(in English) a pile of stones / algorithms / games / number theory / prohibition / strategies / /  
Reference Info. IEICE Tech. Rep., vol. 116, no. 211, COMP2016-17, pp. 17-24, Sept. 2016.
Paper # COMP2016-17 
Date of Issue 2016-08-30 (COMP) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
Copyright
and
reproduction		 All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
Download PDF COMP2016-17

Conference Information
Committee COMP  
Conference Date 2016-09-06 - 2016-09-06 
Place (in Japanese) (See Japanese page) 
Place (in English) Toyama Prefectural University 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2016-09-COMP 
Language English 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Games with a Single Pile of Stones and Number Theoretic Problems 
Sub Title (in English)  
Keyword(1) a pile of stones  
Keyword(2) algorithms  
Keyword(3) games  
Keyword(4) number theory  
Keyword(5) prohibition  
Keyword(6) strategies  
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Keyword(8)  
1st Author's Name Yoshihiro Tsukamura  
1st Author's Affiliation Sony Corporation OB (SONY)
2nd Author's Name Yoshihide Igarashi  
2nd Author's Affiliation Gunma University (Gunma Univ.)
3rd Author's Name Yuta Urabe  
3rd Author's Affiliation Gunma University (Gunma Univ.)
4th Author's Name Koichi Yamazaki  
4th Author's Affiliation Gunma University (Gunma Univ.)
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Speaker Author-3 
Date Time 2016-09-06 13:30:00 
Presentation Time 30 minutes 
Registration for COMP 
Paper # COMP2016-17 
Volume (vol) vol.116 
Number (no) no.211 
Page pp.17-24 
#Pages 8 
Date of Issue 2016-08-30 (COMP) 

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