The numbers in parentheses are the old numbers used in each of the lists of unsolved problems given on pp. 183–189 of AMS Proc. Sympos. Appl. Math. 43 (1991), called PSAM 43 below; on pp. 475–491 of Games of No Chance, hereafter referred to as GONC; on pp. 457–473 of More Games of No Chance (MGONC); and on pp. 475–500 of Games of No Chance 3 (GONC3). Some numbers have little more than the statement of the problem if there is nothing new to be added. References [year] may be found in Fraenkel’s bibliography at the end of this volume. References [#] are at the end of this article. A useful reference for the rules and an introduction to many of the specific games mentioned below is M. Albert, R. J. Nowakowski and D. Wolfe, Lessons in Play: An Introduction to the Combinatorial Theory of Games, A. K. Peters, 2007 (LIP) or Berlekamp, Conway and Guy, Winning Ways for your Mathematical Plays, vol. 1–4, A. K. Peters, 2000–2004 (WW).

Subtraction games with finite subtraction sets are known to have periodic nim-sequences. Investigate the relationship between the subtraction set and the length and structure of the period. The same question can be asked about partizan subtraction games, in which each player is assigned an individual subtraction set. See Fraenkel and Kotzig [1987].