Here is a chess problem that uses retrograde analysis. I’ve also posted it on the “France-Echecs” chess forum, which is in French of course, and on my blog.

[FEN "3qk3/3pp3/8/8/8/3PP3/1PP2PP1/RNBQKBNR w - - 0 1"]

Each of the eight White pieces on the first rank has made exactly three movements, except one of them who made only one. Which piece is it?

  • Ah, yes, much better now — many thanks Rowan! Sep 10 '20 at 22:03
  • Wlecom on Chess.Se, Eric ! (I used to be Puch on France-Echecs)
    – Evargalo
    Sep 11 '20 at 12:20
  • Hello Puch -- I remember your pseudo, indeed, on FE !-) Sep 12 '20 at 15:52
  • Looks fun! Can you clarify what it means for a piece to have made one move? For example, if you play a2-a4, a4-a5, a5-a6, a6-a7, a7-a8=R, Ra8-a1, has the rook made one move or six moves? If we play O-O and then Rf1-Rh1, has that rook made one move or two moves? Sep 13 '20 at 11:40

According to the pawn structure, one of the white bishop must be a promoted one. The knights have switched place, the other pieces can easily make three movements.

The only ones that can make a single one are the rooks, either by

  1. Castling
  2. Taking the other rook's square
  3. By coming from a promoted pawn on a8 or h8

All possibilities seems doable as white can promote two pawns, and can use a captured piece to capture all black pieces.

Here is an example:

[fen "rnbqrnbq/ppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w - -"]

1. d3 a5 2. e3 h5 3. Bd2 b6 4. Be2 g6 5. Bxa5 Bb7 6. Bxh5 Bg7 7. Bxb6 Qc8 8. Bxg6 Kf8 9. Bxc7 Nc6 10. Bxf7 Nf6 11. a4 Nd8 12. h4 Ne8 13. Bxd8 Qxd8 14. Bxe8 Kxe8 15. a5 Qc7 16. h5 Kf7 17. a6 Qd8 18. h6 Ke8 19. axb7 Qc7 20. hxg7 Kf7 21. bxa8=B Qd8 22. gxh8=B Ke8 23. Nc3 Qc7 24. Nf3 Kf7 25. Qd2 Qd8 26. Ke2 Ke8 27. Ra5 Qc7 28. Rha1 Kf7 29. Rh5 Qd8 30. Rhh1 Ke8 31. Qe1 Qc7 32. Kd2 Kf7 33. Qd1 Qd8 34. Ke1 Ke8 35. Ne2 Qc7 36. Nd2 Kf7 37. Nb1 Qd8 38. Ng1 Ke8 39. Bf3 Qc7 40. Bc3 Kf7 41. Bd2 Qc8 42. Be2 Kf8 43. Bc1 Qd8 44. Bf1 Ke8

In this example rook h1 makes a single move while other white pieces on the first row make three moves.

  • 3
    Waow, indeed, nice analysis Étienne — my problem is thus cooked, sorry! Sep 10 '20 at 22:07
  • 3
    @RewanDemontay, yes of course, sorry if it was not clear.
    – Étienne
    Sep 11 '20 at 5:54
  • I will try to fix that -- seems impossible, though !-(( Sep 11 '20 at 12:44
  • Yes, I guess I found a fix yesterday night, watching Zverev beat Carreno Busta (how boring!-) Here is the new FEN (same question: « The pieces on the first rank moved exactly three times, except one on them that made a single move: which one? ») rnbqkbnr/p3pppp/8/8/3PP3/1P3PPP/RNBQKBNR Sep 12 '20 at 15:41
  • It's only now that I see the beautiful animated diagram NN-NN. How was that done? Can I do it myself and publish something like that, in the future? The symmetric solution given is a joy -- bravo Etienne (if Etienne did it)! Sep 12 '20 at 15:50

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