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When I first saw the closing position of this study by David Gurgenidze, I found it difficult to believe. White is a rook and pawn behind, with no threats, and it's Black's move. Yet it's a draw.

Starting in the diagram, it's White to play and draw and his first task is to cope with the threat of Rxb1+. Since 1.Qc2+ Qxc2+ 2.Kxc2 Rxb1 gives Black an easy win, the first move is easy enough: 1.Qf7+ when Kxb1 allows immediate mate on b3. So Black plays instead 1...Kb2 and now what? White will not survive long if he plays 2.Qf6+ Kxb1 3.Qxb6+ Ka2+. Something more drastic is called for.

Well, if you can't find a perpetual check, look for a stalemate. So let's get on with it: 2.Rg2+! Qxg2 3.Qf2+! and if Black takes the queen the goal is achieved. But he needn't oblige, for now it's Black's turn to be clever with 3...Kb3! when 4.Qxg2 loses to Rxb1+ followed by Rb2+.

There is nothing for it but to return to the perpetual check idea: 4.Qxb6+ Ka2 (the only place to hide from an otherwise endless series of checks) and now since Qf2+ no longer gives a stalemate when captured, it has to be 5.Qe6+ Kxb1 6.Qb3+ Qb2.

Now White seems totally lost. After he checks on d3, the black king sidles back to a2, discovering a fatal check from the rook. It seems to be all over, but White has a remarkable resource: 7.Qc4!!

Now if Black's queen moves up the board, then Qc2 will be mate, if she moves sideways, then Qb3+ will force repetition of moves. 7...a2 lets White force mate with 8.Qd3+ so the only try is 7...Ra2 when White plays 8.Qb4!! Ka1 9.Qc3!! Kb1 10.Qb4. If the queen is taken, it is stalemate, otherwise Black cannot escape the merry-go-round. A remarkable draw.