| | o | | o | | o | | | 21 |---------------------------------------| 20 | o | | o | | | | * | | |---------------------------------------| | | * | | | | | | * | 13 |---------------------------------------| 12 | * | | * | | | | | | |---------------------------------------| | | | | * | | | | | 5 |---------------------------------------| 4 | | | | | * | | * | | +---------------------------------------+ 3 2 1

Diagram 114.

Four variations are possible here.  If 31-27 or 30-25, Black wins by (12) 13-17, 22-13; (13) 14-18, etc. (11) ..., 22-17 loses on account of (12) 13-22, 26-17; (13) 14-18.  The sacrifice (11) ..., 21-17; (12) 14-21, 22-18 is met by (13) 10-14, 18-9; (14) 1-5, 26-22; (15) 5-14, 31-26; (16) 13-17.

Black White

(12) 13-17          18-9
(13)  6-13          21-14
(14) 10-17          26-22

In answer to 30-25 Black wins by (15) 7-10, 25-22; (16) 2-6; but with 31-27 White can offer prolonged resistance, thus: 

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

Diagram 115.

(14) ..., 31-27; (15) 17-22, 26-17; (16) 13-22, 19-15; (17) 11- 18, 23-14; (18) 1-6, 20-11; (19) 7-16, 27-23; (20) 16-19, 23-16; (21) 12-19, 24-15; (22) 6-10, 15-6; (23) 2-18, 28-24; (24) 18-23, 24-19; (25) 23-27, 19-15; (26) 27-32. 15-10; (27) 32-27, 10-6; (28) 27-23, 6-1; (29) 22-26, 1-6; (30) 26-31, 6-9; (31) 30-26, 9- 13; (32) 26-22, 13-9; (33) 23-18.  Black has now received first position and wins.

          Black White

(15) 17-26 31-22 (16) 7-10 30-25 (17) 2-6 25-21 (18) 6-9 22-18 (19) 1-5 18-15

White must give up a piece to get through, and Black can then exchange at his leisure and win without difficulty.

          (20) 11-27, etc.

V

PROBLEMS

Checker problems, unlike the Chess problems, are intimately related to the game itself and do not enable combinations different in kind from those which occur in the actual fight over the board.