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Paper Abstract and Keywords
Presentation 2017-10-27 14:00
A Revised Version of "Games with a Single Pile of Stones and Number Theoretic Problems"
Yoshihiro Tsukamura (former Sony), Yoshihide Igarashi, Takaaki Fujita, Yuta Urabe, Koichi Yamazaki (Gunma Univ.) COMP2017-22
Abstract (in Japanese) (See Japanese page) 
(in English) The game MSP(m) discussed in this paper, is played alternately by two players, removing at least one stone and at most $m$ stones from the single pile at each turn. Each player is prohibited from removing the same number of stones as the number of stones removed by the opponent at the immediately previous turn. A player who makes the pile empty wins the game. Furthermore, when a player cannot remove any number of stones due to the prohibition rule, the opponent becomes the winner. This game is denoted by MSP(m). In our previous report [Games with a Single Pile of Stones and Number Theoretic Problems, COMP2016-17 pp.17-24], we formulated the initial numbers of stones, called unsafe number of stones, at the pile such that the second player of MSP(m) is promised to become the winner. However, we discovered that there were some serious errors in the previous report. In this paper, we remove the errors in the previous one, and add some new results. We categorize MSP(m)s into types $1, 2, 3, ..., k, k + 1, ...$ according to certain properties of $m$'s. Then for each type of MSP(m)'s we investigate the periodicity of unsafe numbers. For vast majority of MSP(m)'s, from the periodicity we can efficiently decide which player is promised to become the winner of the game with a given initial number of stones.
Keyword (in Japanese) (See Japanese page) 
(in English) a pile of stones / algorithms / games / number theory / prohibition / strategies / /  
Reference Info. IEICE Tech. Rep., vol. 117, no. 269, COMP2017-22, pp. 13-20, Oct. 2017.
Paper # COMP2017-22 
Date of Issue 2017-10-20 (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 COMP2017-22

Conference Information
Committee COMP  
Conference Date 2017-10-27 - 2017-10-27 
Place (in Japanese) (See Japanese page) 
Place (in English)  
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2017-10-COMP 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) A Revised Version of "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 former Sony Corporation (former Sony)
2nd Author's Name Yoshihide Igarashi  
2nd Author's Affiliation Gunma University (Gunma Univ.)
3rd Author's Name Takaaki Fujita  
3rd Author's Affiliation Gunma University (Gunma Univ.)
4th Author's Name Yuta Urabe  
4th Author's Affiliation Gunma University (Gunma Univ.)
5th Author's Name Koichi Yamazaki  
5th Author's Affiliation Gunma University (Gunma Univ.)
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Speaker Author-3 
Date Time 2017-10-27 14:00:00 
Presentation Time 30 minutes 
Registration for COMP 
Paper # COMP2017-22 
Volume (vol) vol.117 
Number (no) no.269 
Page pp.13-20 
#Pages 8 
Date of Issue 2017-10-20 (COMP) 

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