Proof Game in 8.0

Much can be read from the arrangement of Black’s pieces. The bQ must’ve taken two steps to reach g5 (Qd8–d5, then Qd5–g5), preceded by the d7-pawn advancing twice (d7–d5, d5–d4), and followed by Bc8–f5. Add to that the g8-knight’s three hops (Nf6, Nd5/Nh5, Nf4), and you’ve got all eight of Black’s moves accounted for.

White’s pieces, by contrast, offer little to go on. The f-pawn has moved once; the rest appear untouched. That leaves seven moves unaccounted for — presumably spent on a round trip. But to return to its starting square after an odd number of moves, a piece must lose a tempo, which surely rooks and knights can’t manage. That makes the wK the lone suspect: it must have slipped out via f2, triangulated, and circled back to e1.

But the question remains: how did the wK thread through Black’s forces? The trick must’ve been to defer ...d7–d5 — played too early, it stakes out too many light squares too soon, impeding the wK’s manoeuvrability. That suggests Black began with three moves by Ng8. Let’s test a line: 1.f3 Nf6 2.Kf2 Nh5 3.Ke3 Nf4 4.Ke4 d5+ 5.Kd4 — a dead end. 5...Bf5 can’t come yet, as Qd5–Qg5 must happen first. That implies the triangulation went via g4, with the bN reaching f4 through d5.

Hence, the solution: 1.f3 Nf6 2.Kf2 Nd5 3.Kg3 Nf4 4.Kg4! d5+ 5.Kh4 d4 6.Kg3 Qd5 7.Kf2 Qg5 8.Ke1 Bf5 — and we arrive at the diagram!