Chess

This problem by Walter Grimshaw - a first-prize winner in 1852 - is the sort of composition that convinced me, many years ago, that one should simply look up the answer of a chess problem and enjoy it, rather than trying to find the solution yourself. It is White to play and mate in three.

If you insist on working it out yourself, the first thing you notice is the rook and bishop on the same diagonal as Black's king. There's a discovered check waiting to be played, but doing it at once is pointless: any rook move on the file lets the black king escape to e5; and a move on the rank lets it get away to d4.

Those possibilities should set you off looking at moves that guard e5 or d4. There's 1.Kf6, or 1.Nf5 to begin with, but Black has several defences in either case (you can work them out yourself). There's a temptation to play 1.Nf3 - which has the merit of guarding both the e5 and d4 squares, but Black simply takes it with 1...Kxf3 and there is no mate because f2 is unprotected.

Another idea for White is to play f3+ and mate after Ke3 with Nf5 or Ng2, but that's obviously too far-fetched, because we'd need both f2 and f3 to be protected.

The answer, however, uses precisely that far-fetched idea. White begins with 1.Rf1!! threatening 2.f3+ Ke3 3.Ng2 (or Nf5) mate. After 1...exf1=Q, White continues with the extraordinary 2.Nf3!! when any check from the new queen allows Rg5 mate. Since Re5 mate and Rd4 mate are also threatened, Black must play 2...Kxf3, when 3.Rd2 is mate again - protecting f2 at last.

We now need only to tidy up the details: 1...e1=Q 2.Rd3+ Ke5 3.Rxe1 mate; or 1...f3 2.Rg1! followed by Rg4 mate. Brilliant!