Otto Blathy, better known for his part in inventing the modern transformer, was fond of the chess problem genre called “long-movers”. He once created a problem with the stipulation, “white to play and checkmate in 290 moves” which is still considered the longest such problem. But it sounds more interesting than it actually is because these long problems typically involve repeated king marches by white in order to lose a tempo. Once you grasp the main concept, the whole thing becomes monotonous and boring. What is neither monotonous nor boring is the geometrically longest checkmate that can be delivered on a chessboard : a checkmate that covers the whole of the long diagonal. Just imagine the visually pleasing spectacle of a queen moving to the a1 square to checkmate the enemy king on h8. It’s an extremely rare guest even in the realm of chess compositions. [caption id="attachment_157532" align="alignnone" width="300"] White to play and mate in three moves - Phillip H Williams (1908)[/caption] There is a fairly obvious checkmate in four moves. White can simply play something like 1.Qxh2 Kxa7 2.Qd6 Kb7 3.Rh7+ Kc8 4. Qf8#. To achieve the same objective in one less move is not so straightforward. Now that we know the theme, we can see that it’s a checkmate if we can get the white queen to the long diagonal while somehow protecting the a7 pawn. The solution is delightful, both visually and geometrically. 1.Kb2! a1=Q (or any) 2.Rxa1 h1=Q (or any) 3.Qxh1#. Your columnist came across the following problem nearly a quarter of a century ago in his second year of playing chess. It still resonates strongly because it took more than three months of obsessing over it to solve. [caption id="attachment_157533" align="alignnone" width="300"] White to play and mate in three moves[/caption] Once again, it’s possible to achieve the objective in four moves by ‘normal’ means. For instance,  1.Qg1 Kxh7 2.Nf4 Kh8 3.Ne6 Kh7 4.Qg7#. Our theme should point you in the correct direction to find a mate in one less move. 1.Nb2! cxb2 2.Na1! bxa1=Q 3.Qxa1# Here’s an even tougher, yet truly spectacular problem. Even my computer struggles with this one. [caption id="attachment_157534" align="alignnone" width="300"] White to play and mate in four moves[/caption] First, it’s important to understand the board orientation properly, and yes… those three black pawns are close to getting promoted. The white queen is under attack. Let’s try the natural moves (1.Qg3 and 1.Qh4) to get the queen closer to the business end. 1.Qg3 Rg1 2.Qxg1 a1=Q and 1.Qh4 Rh1 2.Qd8 Rh7 means black has just enough resources to respond. The only option left for white is to try the Nb4-d5-c7 checkmating idea. 1.Nb4 c2 (1...Rxe1 2.Nd5 followed by 3.Nc7#) Now 2.Nd5 won’t work because of 2...c1=Q when the c7 square is covered. So white must come up with a creative idea to stop that. 2.Qc1! [caption id="attachment_157535" align="alignnone" width="300"] 2.Qc1! - A stunning idea[/caption]  Now it looks like the Nd5-c7# is unavoidable, but black springs a surprise. 2… b1=B!  All of a sudden, white can’t execute the intended knight maneuver because of stalemate. But there is enough time and resources for one last twist. 3.Nd3! exd3 4.Qh1#.  The longest checkmate strikes again!  Finally, here’s an unusual problem to bring out your inner Sherlock Holmes. [caption id="attachment_157536" align="alignnone" width="300"] Retract one move and mate - Sam Loyd[/caption] White has just made a move and realized he/she could have given a checkmate instead. What was the move white played and what was the checkmate he missed? Remember that when you retract white’s last move, black’s king cannot be in a check. For instance, you can’t retract Ke2-f1 and play Ng4-f2# instead. If you fail to find the solution, try to remember our theme and try again.