Problems in which no definite number of moves are stipulated for the mate are usually called studies or endings.  They are nothing but game positions in which a maneuver forces the win that is so well hidden that it would probably not be found by a player in an actual game.  The following two positions are examples of this class of compositions.

The first move is evident.  White must play (1) P-c7, as otherwise Black retreats with the Rook in the d-file and occupies the c-file so that he can be sacrificed at any time for White’s dangerous Pawn.

+---------------------------------------+
8 |    |    |    |    |    |    |    |    |
|---------------------------------------|
7 |    |    |    |    |    |    |    |    |
|---------------------------------------|
6 |    | ^K | ^P |    |    |    |    |    |
|---------------------------------------|
5 |    |    |    | #R |    |    |    |    |
|---------------------------------------|
4 |    |    |    |    |    |    |    |    |
|---------------------------------------|
3 |    |    |    |    |    |    |    |    |
|---------------------------------------|
2 |    |    |    |    |    |    |    |    |
|---------------------------------------|
1 | #K |    |    |    |    |    |    |    |
+---------------------------------------+
a    b    c    d    e    f    g    h

Diagram 82.—­White to play and win.

After (1) ..., R-d6+ White can neither go to b7 on account of R-d7 nor can he play K-c6 or c5 on account of R-d1 followed by R-c1 whereby Black would draw.  The only way to win is:  (2) K-b5, R-d5+; (3) K-b4, R-d4+; (4) K-b3, R-d3+; (5) K-c2.  At last White has succeeded in guarding his rear, and it seems as if Black could not any longer prevent the Pawn from Queening.  However, Black plays (5) ..., R-d4 and if White queens the Pawn he gives check on C4 forcing Qxc4 which would stalemate the King.

+---------------------------------------+
8 |    |    |    |    |    |    | ^K |    |
|---------------------------------------|
7 |    |    |    |    |    |    | ^P |    |
|---------------------------------------|
6 |    |    | #B | ^B |    |    |    |    |
|---------------------------------------|
5 |    |    |    |    |    |    |    |    |
|---------------------------------------|
4 |    |    |    |    |    |    |    |    |
|---------------------------------------|
3 |    |    |    |    |    |    |    |    |
|---------------------------------------|
2 |    |    | ^Kt|    |    | #P |    | #P |
|---------------------------------------|
1 |    |    |    | #K |    |    |    |    |
+---------------------------------------+
a    b    c    d    e    f    g    h

Diagram 83.—­White to Move and Draw.

This is the point where the problem-trick enters the game.  White does not promote the Pawn to a Queen but to a Rook, avoiding the stalemate and threatening mate on a8.  Black’s only defense is R-a4 and now White wins by (7) K-b3 attacking the Rook and threatening mate on c1 at the same time.