A game in which the players alternately name positive integers that are not sums of previously named integers (with repetitions being allowed). The person who names 1 (so ending the game) is the loser.
The question is: If player 1 names ‘16’, and both players play optimally thereafter, then who wins?
It has been known that if player 1 name "5n," then player 1 wins. If player name "5n+2", the result is known(maybe palyer 2 wins, but I haven't found the source yet). 16 is the minimum number of "5n+1".
I guess that this problem is PSPACE-hard, but I haven't proved it yet.