
doi: 10.1007/bf01253778
Kayles, first introduced by \textit{H. E. Dudeney} [``Canterbury puzzles'' (London 1910), p. 118, p. 120] and \textit{S. Loyd} [``Cyclopedia of tricks and puzzles'' (New York 1914), p. 232], is an impartial combinatorial game, played with rows of skittles. Two players alternatively remove a single skittle or two contiguous ones. The winner in normal play is the person who removes the last skittle. In misère play this person is the loser. Kayles was one of first nontrivial games to be analyzed [the reviewer and \textit{C. A. B. Smith}, Proc. Cambridge Philos. Soc. 52, 514--526 (1956; Zbl 0074.34503)],using the Sprague-Grundy theory [\textit{R. P. Sprague}, Tôhoku Math. J. 41, 438--444 (1936; Zbl 0013.29004); \textit{P. M. Grundy}, Eureka 2, 6--8 (1939)], which doesn't apply to misère play, whose analysis is much more recalcitrant [\textit{P. M. Grundy} and \textit{C. A. B. Smith}, Proc. Cambridge Philos. Soc. 52, 527--533 (1956; Zbl 0074.34504); the second author, ``On numbers and games'' (1976; Zbl 0334.00004)]. Now Kayles reappears as the first nontrivial game to reveal its misère analysis. Since then \textit{T. Plambeck} [Theor. Comput. Sci. 96, No. 2, 361--388 (1992; Zbl 0777.90095)] has used the Sibert- Conway type of analysis to settle the game of Daisies (Guy-Smith code 4.7) and other games having a similar (normal play) nim-sequence.
Kayles, misère analysis, impartial combinatorial game, Combinatorial games, nim-like games
Kayles, misère analysis, impartial combinatorial game, Combinatorial games, nim-like games
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