He was wearing black trunks and I think he was trying to suck in his stomach. In fact he looked a lot fitter than most men of his age; but I’m afraid I wasn’t paying much attention. Something else – someone else – had caught my eye.

He was poised, arms raised and knees slightly bent, on the diving board at the other end of the pool. He didn’t look in my direction but I knew he had seen me; the pose was designed to show off his tan and the lean lines of his body, and he held it a little too long before he sprang and dived, slipping through the air and into the water as smoothly as a water snake.

I turned to Larry. ‘What the hell – ’

I was so outraged I had forgotten Schmidt. Larry’s raised hand reminded me. Schmidt was trotting towards the pergola, but if I’d gone on at the same volume he would have heard me.

‘It’s as difficult to get out of this place as it is to get in,’ Larry said quietly. ‘I’d rather have him here, where I can monitor his activities, than on the loose in Luxor.’

‘He’s not stupid enough to make any false moves here,’ I insisted. ‘He knows he’s under suspicion.’

‘Stupid, no.’ Larry’s eyes were focused on John, who had pulled himself out of the water and was sitting on the edge of the pool. Schmidt came trotting up to him, waving a glass and calling out enthusiastic greetings. Smiling in response, John leaned back, supporting himself on his elbows. The movement stretched the muscles of his chest over the underlying structures of ribs and clavicles. He had lost weight – not much, he had never had much to lose, but those elegant bones were more visible now.

‘Stupid, no,’ Larry repeated. ‘Arrogant, yes. If we give him enough rope . . .’

‘His complexion is perfect gallows.’ I had proposed that once, as a fitting epitaph for John. Did they hang people in Egypt?

‘I need a drink,’ I said.

John slid back into the water. Schmidt peeled off his robe, flung it aside with the panache of Arnold Schwarzenegger (whom he did not in the least resemble), pinched his nose with two fat fingers, and leaped into the pool. A fountain of water billowed skyward. Averting my eyes, I followed Larry towards the pergola. Mary was there, stretched out on a deck chair, half-hidden by sprays of jasmine, and not much else. Her suit was very French – a few patches and a few strings. In her case the effect was cute rather than sexy; she was shaped as delicately as a child. Not a bulge anywhere.