Correct me if I am wrong.
Diagram #1 by Alex
White to move.
When we examine the available moves for white we see right away that 13-9 loses two men by way of 6x22. There are only two other moves for white and 23-18 gives away the man so 23-19 seems to be the correct move here. Looking further we see if black then moves 6-9 his man is lost and 10-15 will give white two of his men by either 19x1 or 17x1 so black only has two choices left to him, we see that 20-24 allows white a 2 for 1 shot (19-15, 10x19, 17x1). Therefore, 14-18 is the only move left to black and will give us this position.
White has 4 possible moves here, 19-15 will lose the man by way of 10X19, 19-16 looks as if it will lead to a drawn game, again 13-9 will still give away 2 men by way of 6X22. White's last possible move is the 17-14, 10X17, 21X14 trade. Looking further we see that this trade leaves black's man on 6 trapped and will force black to advance one of his remaining two men forward to the king row on his next move, either 18-22, 18-23 or 20-24. After black's move white can put more pressure on black's man on 6 by moving 19-15. Black's only option will again be to advance one of his other men toward the king row and white can then squeeze his man on 14 onto square 9 (14-9) or onto square 10 (14-10) either way white gets the same result, black's man on 6 will be captured after black make his next move and there is nothing black can do to stop white.
Regards, "Pal" Bucker
CHECKERS: The Mind Sport of Kings and Ordinary Men.