Virtually every beginning chess problem solver asks early on, "How could a game ever come to this position?"

The answer is that problems are puzzles and are not really related to the game of chess. The solver needs no more than a knowledge of the rules of chess and a willingness to be intrigued, amused and startled.Any player of any strength can enter the fascinating realms that concern the chess "problemist." Relaxation and pleasure can be derived both from the game of chess and from chess problems.

Perhaps the first point that strikes a newcomer to problems is that, like correspondence chess, the problemist has and needs no partner physically present on the other side of the board.

Whether he constructs a problem, as a "composer," or unravels its secrets, as a "solver," he alone deploys the white and black men before him, or in his mind's eye.

The problemist in the lonely crowd of computers or in his hospital bed always has an avenue of escape. This is not to imply that problems are designed solely for hermits. There is great fraternity, through clubs, publications and prizes among and between problemists.

What is a chess problem? There are various answers, but as a working definition, the problem, like those published in this column, is the term assigned to a composed position in which White, by convention moving first and up the board as diagrammed, must force the checkmate of Black in a stipulated maximum number of moves, always two moves in this column.

This number refers to "White." Thus, "Mate in two" means, "White moves - Black makes any reply - White now checkmates Black." Problems that run like this are termed "two-movers" (again, reference is to the number of moves by White). "Mate in three" means that White must checkmate Black with his, White's, third move at the latest. A problem of this kind is a "three-mover."

An important point underlying all this is that every problem presents not just a win for White but his win by checkmate and within a fixed number of moves by him.

Many problem positions show a predominant white army, and are self-evidently "won for White," as a player would put it, but this is not the issue.

What the solver must seek, in each case, is that frequently elusive, maybe pleasingly surprising first move, the "key" as it is termed, that enables the mate of Black to be achieved whatever Black does and before the stated number of White is exceeded.

The discipline of the player's remorselessly ticking clock is thus paralleled in problems by a quite different kind of challenge. For example, problems designated "miniature" must stay within the total number of men, white and black together, and must not exceed seven.

Our problems are of the so-called "direct-mate" kind. This means that they use the board, men and rules of chess familiar to the player, with the same purpose as in the game: to checkmate an opposing party.

Remember, however, in these problems, White always wins! Castling by either side is permitted unless it can be proved illegal, e.g., because of a prior move by the respective king or rook.

The concept of legality is applied to a problem more generally in that the latter is expected to represent a position to which a hypothetical game could have led. This means, of course, that the white king always stands on the board, even if he takes no part in the downfall of his black counterpart.

Or, again, to take a random constructional point, if a white pawn occupies B2, a white bishop cannot stand on A1, as it "could never have got there."

Other connections between the problem and game, over and above basic legality, are recognized by the chess player. Thus the brilliant sacrifice of over-the-board play is a routine, but still attractive, device in problems.

- CONGRATULATIONS TO THE SOLVERS! - William DeVroom, Kim Barney, Russell Anderson, David Moody, Stanley Hunt, Edwin O. Smith, Ted Pathakis, Hal Harmon, Hal Knight, Robert W. Lee, Ardean Watts, Ashley Ann Graves, Kay Lundstrom, Gordon Green, Eugene Wagstaff, Jack Crandall, Alison Hermance, Raeburn Kennard, Aaron T. Kennard and Jim Reed.