Joseph Ney Babson (1852-1929) bequeathed to the world of chess problemists a challenge - known as the Babson Task - that was to keep them occupied for more than 50 years after his death. The task was to compose a problem in which White and Black both have a pawn on the seventh rank, and in reply to four variations in which the black pawn promotes to queen, rook, bishop and knight, White must promote to the same piece in each case to force mate.

Babson had done it in a non-standard problem - a self-mate where White had to force Black to give mate - but composers despaired over attempts to do it in the standard, White to play and mate in n, format.

For fifty years the Babson task was thought impossible, but in 1983 the Russian Leonid Jarosh cracked it. The diagram shows his extraordinary composition. It is White to play and mate in four.

The first move is 1.a7! setting up the mechanism. After 1...axb1(Q) White plays 2.axb8(Q)! Qxb2 (giving the king an escape square on d3) 3.Qxb3! Qxa1 4.Rxf4 mate.

After 1...axb1(R), 2.axb8(Q)? Rxb2 3.Qxb3 is stalemate; but White plays 2.axb8(R)! Rxb2 3.Rxb3 Kxc4 4.Qa4 mate.

Still more tricky is 1...axb1(B), when Black introduces the idea of Be4 into the defence. The only way to defeat it is 2.axb8(B)! Be4 3.Bxf4! Bxa8 4.Be5 (or Be3) mate.

The last thematic variation is 1...axb1(N) 2.axb8(N)! Nxd2 3.Qc1 Ne4 (otherwise 4.Rxf4 will be mate) 4.Nc6 mate.

Finally, and somewhat messily, we have to fill in the details of the mates if Black does not promote his pawn at the first move: 1...Qxd8+ 2.Kg7! Qc7 3.d8=Q+ Qxd8 4.Rxf4; or 1...Qe5 2.Bxe7 Qd6 3.Nxd6 axb1(Q) 4.Bxf6 mate; or 1...Qxa8 2.Rxf4+ Qe4 3.a8=Q Qxf4 4.Qd5 mate; or 1...Qd6 2.Re1 Qe5 (to stop Re4 mate) 3.Nxe5 fxe5 4.Re4 mate.

The magnitude of this achievement (and the fact that Yarosh went on to publish a slightly simpler version soon after) must make this a candidate for the Greatest Problem of All Time award.