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This splendid problem by Kraemer and Zepler won first prize in a composing tournament in 1935. It is White to play and mate in three.

With Black's king surrounded, it looks as though it ought too be easy, but most mating attempts run into the same problem: as soon as White moves his knight from f6 to open the line from his queen to the black king, he runs into a discovered check on the f-file. White could eliminate the troublesome knight with 1.Rxf5, but that abandons the rook's defence of the d7-pawn and lets Black survive until beyond move three with 1...Rxf6.

What White needs is either another way to get at the black king with his queen, or a way to get his own king away from the problems on the f-file. The solution accomplishes this in an astonishing manner.

White begins 1.Ke1!! apparently walking into a variety of ambushes; but look what happens. The threat is 2.Ng4+ Nxh6 3.Ne5 mate. If 1...c1=Q+ 2.Qxc1 h1=Q+, White mates with 3.Bg1. (Or if Black checks with a rook on e8 on the second move od this line, then 3.Be3 is mate).

If Black tries promoting his pawns the other way round with 1...h1=Q+ 2.Qxh1 c1=Q+, then 3.Rd1 is mate (or 2...Re8+ 3.Re5 mate). Finally, and perhaps most difficult to spot, if 1...Rae8+ 2.Nxe8+ Rf6, White mates with 3.d8=N!

The idea of walking White's king into a barrage of checks is reminiscent of another classic three-move problem by Sam Loyd.

Here White is ready to deliver discovered checks on the fifth rank and on the long black diagonal, but his difficulty lies in providing a guard for the e4 and d4 squares. The main line of the solution is quite extraordinary: 1.Ke2!! f1=Q+ 2.Ke3!! when any check from the black queen, bishop or rook is met by a discovered mate. The other variations I leave you to work out on your own.