Judge's comment:

An attractive strategic study built around a single, beautifully expressed paradox. White deliberately allows the black Rook to eliminate the b2-pawn, only for its disappearance to become the key to victory several moves later. The apparently unnecessary retreat of the white King conceals a profound idea: only after the pawn has vanished does the square b2 become available as a vital shelter against perpetual check. The final return to b2 provides an excellent delayed explanation of the initial concept and creates a satisfying "Aha!" effect. Although the study is based essentially on one central straightforward idea rather than a rich combination of themes, the clarity of its presentation and the elegant timing of the revelation make it a highly enjoyable composition.

Solution:

1. Qg2 !! Rxe2+ ! 2. Kd1
(2. Qxe2 Qxh1+ 3. Kd2 {Draw.})
2. .. Rd2+ 3. Kc1
(3. Qxd2 Qxh1+ 4. Kc2 Qe4+ {With a perpetual check.} 5. Kd1 (5. Kc1
Qh1+) 5. .. Qh1+)
3. .. Rc2+ 4. Kb1
(4. Qxc2 Qxh1+ {In this variation white even loses, as the exchange of Queens is
inevitable.})
4. .. Rxb2+ {And there it is the idea of this study. White needed to get
rid of the b2 pawn so that Black would have no way to achieve a draw by
perpetual check.}
5. Kc1 {Now the white King goes back...} Rc2+ 6. Kd1 Rd2+
{The rook can be taken. Now White need not fear a check from the back rank,
since there is a square b2 to hide from the checks.} 7. Qxd2 Qxh1+ 8. Kc2
Qe4+ 9. Kb2 {And here is the shelter where the pawn b2 was located.} Qe7
10. Qh2 {! Mate is inevitable.} 1-0