Abstract
Finitely many coins are placed on distinct squares of a semi-infinite linear board ruled into squares numbered 0, 1, 2,… Each of the two players alternately moves a coin to a lower unoccupied square, at most k squares from its present position, where k is an arbitrary fixed positive integer. The player first unable to move loses and his opponent wins. We give complete solutions for the case of two coins for any k; and for any number of coins when k = 2 m − 1 ( m ⩾ 1). We also prove that, for any k, the Sprague-Grundy function of the game is invariant under translations of coins by k + 1.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.