Problem No. 1.  White to move and draw.

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

Diagram 116.

They usually represent an end game and are distinguished from ordinary endings only by an unexpected initial move, mostly embodying a sacrifice of several men.  Diagrams 116, 117 and 118 furnish some examples: 

Problem No. 2.  White to move and win.

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

Diagram 117.

If, in Diagram 116, White tried to reach the King row with his man 27, Black would win by first position thus:  (1) . . ., 27-23, (2) 16-20, 24-19; (3) 20-24, 19-15; (4) 24-27, 23-19; (5) 27-24, 19-16; (6) 24-19, etc.  The only way to draw is to sacrifice first the man on 21 by 21-17; and then to continue as above.  This enables White to play 23-18, instead of 19-15, exchanging the King for a man.

The first move in Diagram 117 is 24-28, to which Black must reply (2) 29-25.  White then sacrifices his three men by 17-14 and after (3) 25-27 (or 9-27) plays 28-32.  Black must take the third man, and White recaptures two men by 32-14, pinning both of the remaining black men.

Problem No. 3.  Black to play and win.