The Lacny cycle, also known as the Lacny cycle problem theme, was introduced by Ľudovít Lačný, a Slovak chess problem composer and judge, in 1949. This concept exemplifies a cyclical relationship between lines of play in chess. In one stage, the Black defenses a, b, and c are countered by the White mates A, B, and C respectively. In another stage, the very same defenses a, b, and c are met with the White mates B, C, and A respectively, forming a recurring pattern.
Let’s demonstrate this concept on the original Lačný’s study:
First, we will define the set-up. If it is Black’s turn to move, the problem would start with three different moves, followed by a different checkmate delivered by White (which we mark as A, B, and C):
- 1. … ♞h2 2. ♕d4# (A)
- 1. … c1=♛ 2. ♘g2# (B)
- 1. … c3 2. ♕e4# (C)
Good! Let’s proceed with the actual problem. White to move and mate in two, while the checkmate patterns will be cycled by one position:
As we can see, White made a move 1. ♘d2, threatening 2. ♘f1#. Black will counter it with the moves from the set-up:
- 1. … ♞h2 2. ♘g2# (B)
- 1. … c1=♛ 2. ♕e4# (C)
- 1. … c3 2. ♕d4# (A)
The study received the top accolade at the 1949 Przepiorka Memorial, and it has been widely replicated since then.