Combinatorics · Combinatorial games · Winning and losing positions · Mirroring strategy · Disjoint sums of games · Primes
A pile of \(n\) tokens lies on a table. Two players, \(A\) and \(B\), move alternately, and \(A\) moves first. In one move a player must do one of the following:
- remove one token from one of the piles on the table, or
- replace one of the piles by several piles - at least two of them - all containing the same number of tokens.
A pile whose last token is removed ceases to exist. The player who takes the last token from the table wins.
For which values of \(n\) does player \(A\) have a winning strategy, and for which values of \(n\) does player \(B\) have a winning strategy?
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Serbian National Competition (Drzavno takmicenje) 2014, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source