During the recent development of combinatorial game theory many more problems have been suggested than solved. Here is a collection of problems that many people have found interesting. Included is a discussion of recent developments in these areas. This collection was started by Richard Guy in 1991, and has been updated in each Games of No Chance volume. The problems are divided into five sections:

• A. Taking and breaking

• B. Pushing and placing pieces

• C. Playing with pencil and paper

• D. Disturbing and destroying

• E. Theory of games

In the sections, the problems are identified by letters and numbers. Any number in parenthesis is the old number 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.

Previous versions of the unsolved problems can also be found on pp. 457–473 of More Games of No Chance (MGONC); pp. 475–500 of Games of No Chance 3 (GONC3); and pp. 279–308 of Games of No Chance 4 (GONC4).

Some problems have little more than the statement of the problem if there is nothing new to be added. References [#] are at the end of this article. Useful references for the rules and an introduction to many of the specific games mentioned below are:

• • M. Albert, R. J. Nowakowski, and D. Wolfe, Lessons in Play: An Introduction to the Combinatorial Theory of Games, A K Peters, 2007 (LIP);

• • Berlekamp, Conway, and Guy, Winning Ways for your Mathematical Plays, vol. 1–4, A K Peters, 2000–2004 (WW);

• • Siegel, Combinatorial Game Theory, American Math. Society, 2013 (CGT).

The term “game” is ambiguous and needs to be clarified. If a board is not specified then the question pertains to all possible boards. Berlekamp noted that many games have a standard opening position, an empty board for example. However, some results include positions, such as Garden-of-Eden positions, that could never occur by any sequence of moves from a standard opening position, and ones which would never occur in decent play. Indeed, Plambeck has asked at several meetings whether there is any difference in the complexity results for all positions and those that would occur in decent play.