Charles Leonard Bouton

“ For one of the piles must be reduced to zero by either A or B. If B reduces it to zero, the two remaining piles will be unequal, since B can never leave a safe combination, and A at his next move will make them equal, and will thereafter always leave them equal. B must, therefore, reduce the second pile to zero, and A then takes all of the third pile, and wins. If, on the other hand, A is the first player to reduce one of the piles to zero, he leaves the other two piles equal and wins as before. Hence we see that the player who can first leave a safe combination on the table should win. ”

“ In order to complete it, we must show that B can never leave 1,1,1; that, when 1,1,0 is indicated for A, he can always play either 1,0,0 or 1,1,1; and finally that, if the play is carried out in this way, B must take the last counter. ”