3 problems

Let $p$ be the number of spots in the starting position of a game of Sprouts, and let its nimber be the associated Sprague–Grundy value. Nimber conjecture. The nimber for the start…

Let $S_p^-$ denote the misère version of Sprouts starting with $p$ spots. Period-six conjecture for misère Sprouts. The first player has a winning strategy in $S_p^-$ if and only i…

Let $S_p^-$ denote the misère version of Sprouts starting with $p$ spots. Applegate–Jacobson–Sleator conjecture. The first player has a winning strategy in $S_p^-$ if and only if…