‘None whatever.’

‘I might make a suggestion. Your name!’

‘My name?’

‘Yes. Cust is saddled—apparently by the whim of his mother (Oedipus complex there, I shouldn’t wonder!)—with two extremely bombastic Christian names: Alexander and Bonaparte. You see the implications? Alexander—the popularly supposed undefeatable who sighed for more worlds to conquer. Bonaparte—the great Emperor of the French. He wants an adversary—an adversary, one might say, in his class. Well—there you are—Hercules the strong.’

‘Your words are very suggestive, doctor. They foster ideas…’

‘Oh, it’s only a suggestion. Well, I must be off.’

Dr Thompson went out. Japp remained.

‘Does this alibi worry you?’ Poirot asked.

‘It does a little,’ admitted the inspector. ‘Mind you, I don’t believe in it, because I know it isn’t true. But it is going to be the deuce to break it. This man Strange is a tough character.’

‘Describe him to me.’

‘He’s a man of forty. A tough, confident, self-opinionated mining engineer. It’s my opinion that it was he who insisted on his evidence being taken now. He wants to get off to Chile. He hoped the thing might be settled out of hand.’

‘He’s one of the most positive people I’ve ever seen,’ I said.

‘The type of man who would not like to admit he was mistaken,’ said Poirot thoughtfully.

‘He sticks to his story and he’s not one to be heckled. He swears by all that’s blue that he picked up Cust in the Whitecross Hotel at Eastbourne on the evening of July 24th. He was lonely and wanted someone to talk to. As far as I can see, Cust made an ideal listener. He didn’t interrupt! After dinner he and Cust played dominoes. It appears Strange was a whale on dominoes and to his surprise Cust was pretty hot stuff too. Queer game, dominoes. People go mad about it. They’ll play for hours. That’s what Strange and Cust did apparently. Cust wanted to go to bed but Strange wouldn’t hear of it—swore they’d keep it up until midnight at least. And that’s what they did do. They separated at ten minutes past midnight. And if Cust was in the Whitecross Hotel at Eastbourne at ten minutes past midnight on the morning of the 25th he couldn’t very well be strangling Betty Barnard on the beach at Bexhill between midnight and one o’clock.’

‘The problem certainly seems insuperable,’ said Poirot thoughtfully. ‘Decidedly, it gives one to think.’

‘It’s given Crome something to think about,’ said Japp.

‘This man Strange is very positive?’

‘Yes. He’s an obstinate devil. And it’s difficult to see just where the flaw is. Supposing Strange is making a mistake and the man wasn’t Cust—why on earth should he say his name is Cust? And the writing in the hotel register is his all right. You can’t say he’s an accomplice—homicidal lunatics don’t have accomplices! Did the girl die later? The doctor was quite firm in his evidence, and anyway it would take some time for Cust to get out of the hotel at Eastbourne without being seen and get over to Bexhill—about fourteen miles away—’