THE THIRD POSITION

              32 31 30
       +———————————————————-+
       | | | | | | | | | 29
       |———————————————————-|
    28 | o | | | | | | | |
       |———————————————————-|
       | | | | | | | | | 21
       |———————————————————-|
    20 | oo | | ** | | | | | |
       |———————————————————-|
       | | | | | | | | | 13
       |———————————————————-|
    12 | oo | | ** | | | | | |
       |———————————————————-|
       | | | | | | | | | 5
       |———————————————————-|
     4 | | | | | | | | |
       +———————————————————-+

3 2 1

DIAGRAM 98.—White to Move and Win.

White being a man ahead appears to have an easy win; but owing to the difficulty of getting the man crowned he has a hard task before him.

If the Kings on 11 and 12 were removed White would not be able to win at all, as the Black King would go back and forth between 19 and 23. It is, therefore, clear that in forcing a win from the position of the diagram the King on 12 must cooperate.

Another point to be borne in mind is that the following position would be a draw with White to move.

              32 31 30
       +———————————————————-+
       | | | | | | | | | 29
       |———————————————————-|
    28 | | | | | | | | |
       |———————————————————-|
       | | | | | | | | | 21
       |———————————————————-|
    20 | o | | oo | | oo | | | |
       |———————————————————-|
       | | | | | | | | | 13
       |———————————————————-|
    12 | | | ** | | | | | |
       |———————————————————-|
       | | | | | | | | | 5
       |———————————————————-|
     4 | | | ** | | | | | |
       +———————————————————-+
                    3 2 1

DIAGRAM 99.

White is unable to make any headway because he cannot threaten an exchange. The method in which White threatens the exchange of the King on 19 in the example of third position given in Diagram 98 is the following:

Black White (1) … 20-24 (2) 11-15 24-27

12-8 would be of no use as 19-23 would force 8-12 again.

(3) 15-11

If 15-18 White wins by 27-31

(3) … 27-32

27-31 would admit of a draw by (4) 19-23, 28-24; (5) 23-27, 24- 20; (6) 27-23, 12-16; (7) 11-15, etc.

(4) 11-15 12-8 (5) 15-18 32-27 (6) 18-15 27-31 (7) 15-18 8-11 (8) 18-23 11-7 (9) 19-15

This is better than allowing the Kings to get together.

(9) … 28-24 (10) 23-27 24-20 (11) 27-23 7-2 (12) 15-11 2-6 (13) 23-19 6-10

If he moved the other King, Black would draw by 19-16.

(14) 19-23 10-14 (15) 23-19

Black would lose easily if he allowed the man to advance

(15) … 14-18

Threatening to exchange

(16) 19-24

The only move to avoid the exchange.

(16) … 18-23 (17) 24-28 23-19 (18) 28-32 31-26 (19) 32-28 26-23 (20) 28-32 23-18 (21) 32-28 19-15 (22) 11-8 20-16

and White cannot be prevented from getting another King.

An earlier setting of third position is shown in Diagram 100.

              32 31 30
       +———————————————————-+
       | | o | | | | o | | | 29
       |———————————————————-|
    28 | | | * | | * | | | |
       |———————————————————-|
       | | | | * | | | | | 21
       |———————————————————-|
    20 | | | oo | | | | | |
       |———————————————————-|
       | | | | | | | | | 13
       |———————————————————-|
    12 | | | | | | | | |
       |———————————————————-|
       | | | | | | | | | 5
       |———————————————————-|
     4 | | | | | | | | |
       +———————————————————-+
                    3 2 1

DIAGRAM 100.

White wins by

(1) … 19-24 (2) 27-31 32-28 (3) 23-27 30-23 (4) 27-32 23-18 (5) 32-27 24-20 (6) 27-23 19-15, etc.