Chess: Visitor's irritating conundrum

'White to play, mate in five,' said the Estonian gentleman with the walrus moustache. Toivo Lukats was visiting relatives in England and eagerly pursuing chess-playing opportunities. He spent his last day competing in a one-day quickplay in Highbury, filling in the time between rounds by setting me, and anyone else interested, brilliantly irritating problems to solve, writes William Hartston.

We sat staring at this mate in five for several minutes without even beginning to form an idea. Our first thought was 1. Rd3 d4 2. c4 d5 3. c5 d6, because that is the sort of thing that problemists like, but it leads nowhere. Then we became more serious and started looking for mating positions. 'Use the black pawns as a wall in a mating net,' someone suggested. But there is no way even to get close to such a formation.

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Then I had an idea. There is a mate with the knight on g5, pawn on h3 and rook on f3. But 1. Rd3 d4 2. Nh3+ Ke4 leaves the rook under attack, while 1. Rg3 d4 2. Nh3+ Ke4 3. Ng5+ fails after either king move.

So I had another idea: 'Tell us the answer,' I said. Mr Lukats pushed the rook to d3, and we moved the pawn to d4. 'Now it's c4, yes?' asked someone. 'No,' he was told, and the move 2. cxd4 was made on the board, followed by Black's d5. 'Now it's mate in three,' said the Estonian. We continued to stare for some minutes before finding the answer. Black's fourth move will be d6, after which his king must move. White's knight holds e4 and g4, the rook holds the third rank, so we have to make the king and h-pawn develop their roles. If the king moves we may need something else to guard g5, and that is the final clue. The complete answer is 1. Rd3 d4 2. cxd4 d5 3. h4] d6 4. Kf7] Kf5 5. Rf3 mate. Very neat and surprising.