Chess problems vs puzzles and more on ‘The Queen’s Gambit’ scene

The terms chess puzzles and chess problems may seem synonymous at first glance, but when used precisely, there’s actually a world of difference between them. Both terms refer to special positions in which solvers try to uncover the known “best” moves; but whereas puzzles are tactics exercises derived from actual games, problems are constructed from scratch – i.e. a composition – to show a specific idea. Since it’s not unusual for players unfamiliar with problems to conflate the two types or misunderstand the point of compositions, I want to highlight their important differences and correct some common misconceptions. My earlier blog, Chess problem scene in ‘The Queen’s Gambit’, touched on the subject but did not elaborate. We will revisit that scene from the TV series here as it exemplifies the issues well.

Both puzzles and problems are fun to solve, and they are challenging because a unique move must be found at each step of the solution. Nonetheless, they have different underlying purposes. Puzzles hone your skills at spotting tactics in games, and thus serve as a training tool. Problems are designed to express a theme or artistic idea in their solutions, so their main functions are not utilitarian but aesthetic. See What is a Chess Problem? for some examples that illustrate the concept of themes. Chess problems, in fact, exist as an art form with its own theory, literature, and history distinct from the practical game. The loftier goals of problemists are why they almost never refer to their creations as mere “puzzles,” even if a chess problem is a type of puzzle in the generic sense. Compositions do have puzzle aspects, such as degree of difficulty, but the latter is just one consideration out of many in determining a problem’s worth.

In episode 6 of ‘The Queen’s Gambit’, the protagonist Beth Harmon is introduced to Hilton Wexler who presents a three-move problem for her to solve. She claims not to have attempted problems before, and some viewers were apparently baffled by how a strong player like her could say that, and deemed such inexperience as implausible. This criticism is of course invalid, as it’s based on a confusion between puzzles and problems. Nowadays chess puzzles are ubiquitous (especially online), a go-to resource for improving your game or demonstrating your tactics prowess, but that was hardly the case in the 1960s, when the story was set. While tactics exercises existed in print then, other training methods, like analysing master games, would have been far more prevalent. In that scene, puzzles are simply not in Beth’s mind or anyone else’s, including Hilton the “problem freak” (not a “puzzle freak”) who duly arranged a composition on the board.

The real issue with the scene is the dismissive attitude of Beth (and other characters) towards composed problems; she regards them as “irrelevant” because their positions don’t come up in actual games. While this view is not unusual among regular players, being master-level she should have been more knowledgeable about how problems are a complex field of its own and that they are not meant to resemble game positions. Chess compositions are art for art’s sake, akin to fiction, drama, movies; they are called “the poetry of chess” for good reason. It’s naive to claim that something has to be didactic or “realistic” to be worthwhile, a bit like a documentary maker dismissing all fictional movies as irrelevant or artificial.

There is a major form of composition, separate from the forced-mate problems we’re discussing, that involves more game-like positions – the endgame study. Studies work well as advanced puzzles and top trainers do advise players to practise solving them. Less experienced players sometimes mix up the different conventions of problems and studies, and coupled with a tendency to treat engine analysis as gospel, this would lead them to misconstrue some sound studies as incorrect or even “refuted.” This relates to an even more common belief that some tactics puzzles are faulty because the opposing side makes “sub-optimal” moves. My next blog will diagnose these sorts of claims.

Back to ‘The Queen’s Gambit,’ another flaw in the scene is the choice of the three-move problem. This is supposed to be the favourite of Hilton, a problem aficionado, and yet it’s an ordinary composition rendering a slight idea. There are plenty of prize-winning works, classic or modern, that would have been more appropriate to use. This TV show famously employed top players and experts as consultants, but clearly no problem specialists or composers were among them.

Let’s take a closer look at the problem in question. It’s a directmate, meaning the task is for White to start and deliver mate in the fewest number of moves, against any defence. It is important to specify the number of moves needed to the solver in the stipulation, in this case “Mate in 3 moves.” If a directmate problem got (mis)treated as a tactics puzzle with no stipulation given, the result would be needless confusion or even doubt on the validity of the solution.

Thus, suppose Beth was not told of the “Mate in 3” task; she could then reasonably assume the goal is just to win in the position. Since White is two knights up in material, the win is trivial and there are countless ways to finish off Black, meaning she would be right to say it’s a rather pointless position. But as she was given the three-move task, the position definitely has a point because (among other things) there’s only one way to accomplish it. And not just for White’s initial key-move, but in multiple variations, White’s correct second moves and final mating moves are all precisely forced. Compare this to tactics puzzles which also require unique winning moves, but most involve merely one precise variation of a few moves. What this means is that, broadly speaking, composed problems take the idea of unique play to a new level.

As a composition, the best variation of this problem is (after 1.Kd7!) 1…Kg7 2.Sd6 Kh6 3.Sxf5, because it ends with an elegant model mate. In this type of mating position, every square next to the black king is singly guarded or blocked, and every white piece on the board takes part in the confinement, with the possible exceptions of the king and pawns. The Bohemian style of composition, dating from the 19th century, favoured such visually appealing mates. One reason why this three-move problem is a weak selection is that even when it was originally published, more ambitious works achieving multiple model mates were already flourishing. As an example, here’s another vintage three-mover with similar economy that brings about three models (the record number would be much higher). It’s not top-notch and still unlikely to be the favourite of someone like Hilton, but it’s a gem and a better demonstration of problem art.

How to corral the black king in the middle of the board is far from obvious, as evidenced by the many try-moves refuted by a single defence: 1.Kg6? Kxf4!, 1.Qa5+? Kxf4!, 1.Qb8+? Kf5!, and 1.Qc8? Kxe4! The key 1.Qf8! (waiting) prevents the king from accessing f4 and f5 (this is viewed as unsubtle), but compensates by unguarding the e4-knight. 1…Kxe4 is answered by another sacrificial move, 2.Kf6, which leads to two sub-variations. Taking the offered knight, 2…Kxf4, allows 3.Qb4, an ideal-mate finish; this is a special type of model mate, one in which all units on the board participate in restricting the king. 2…Kd4 also permits 3.Qb4; while the repeated queen move is a small blemish, the model-mate configuration is clearly distinct. Lastly, 1…Kd4 2.Qe8 Kc4 3.Qa4 yields a third model. Hence we discover three attractive mating pictures, which varyingly involve none, one, and both of the knights.