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‘A fast car,’ suggested Tommy.

‘H’m,’ said Tuppence. ‘It is just on two hundred miles.’

‘Australians, I have always been told, drive very recklessly.’

‘Oh, I suppose it could be done,’ said Tuppence. ‘She would arrive there about seven.’

‘Are you supposing her to have nipped into her bed at the Castle Hotel without being seen? Or arriving there explaining that she had been out all night and could she have her bill, please?’

‘Tommy,’ said Tuppence, ‘we are idiots. She needn’t have gone back to Torquay at all. She has only got to get a friend to go to the hotel there and collect her luggage and pay her bill. Then you get the receipted bill with the proper date on it.’

‘I think on the whole we have worked out a very sound hypothesis,’ said Tommy. ‘The next thing to do is to catch the twelve o’clock train to Torquay tomorrow and verify our brilliant conclusions.’

Armed with a portfolio of photographs, Tommy and Tuppence duly established themselves in a first-class carriage the following morning, and booked seats for the second lunch.

‘It probably won’t be the same dining car attendants,’ said Tommy. ‘That would be too much luck to expect. I expect we shall have to travel up and down to Torquay for days before we strike the right ones.’

‘This alibi business is very trying,’ said Tuppence. ‘In books it is all passed over in two or three paragraphs. Inspector Something then boarded the train to Torquay and questioned the dining car attendants and so ended the story.’

For once, however, the young couple’s luck was in. In answer to their question the attendant who brought their bill for lunch proved to be the same one who had been on duty the preceding Tuesday. What Tommy called the ten-shilling touch then came into action and Tuppence produced the portfolio.

‘I want to know,’ said Tommy, ‘if any of these ladies had lunch on this train on Tuesday last?’

In a gratifying manner worthy of the best detective fiction the man at once indicated the photograph of Una Drake.

‘Yes, sir, I remember that lady, and I remember that it was Tuesday, because the lady herself drew attention to the fact, saying it was always the luckiest day in the week for her.’

‘So far, so good,’ said Tuppence as they returned to their compartment. ‘And we will probably find that she booked at the hotel all right. It is going to be more difficult to prove that she travelled back to London, but perhaps one of the porters at the station may remember.’

Here, however, they drew a blank, and crossing to the up platform Tommy made inquiries of the ticket collector and of various porters. After the distribution of half-crowns as a preliminary to inquiring, two of the porters picked out one of the other photographs with a vague remembrance that someone like that travelled to town by the four-forty that afternoon, but there was no identification of Una Drake.

‘But that doesn’t prove anything,’ said Tuppence as they left the station. ‘She may have travelled by that train and no one noticed her.’

‘She may have gone from the other station, from Torre.’

‘That’s quite likely,’ said Tuppence, ‘however, we can see to that after we have been to the hotel.’

The Castle Hotel was a big one overlooking the sea. After booking a room for the night and signing the register, Tommy observed pleasantly.

‘I believe you had a friend of ours staying here last Tuesday. Miss Una Drake.’

The young lady in the bureau beamed at him.

‘Oh, yes, I remember quite well. An Australian young lady, I believe.’

At a sign from Tommy, Tuppence produced the photograph.

‘That is rather a charming photograph of her, isn’t it?’ said Tuppence.

‘Oh, very nice, very nice indeed, quite stylish.’

‘Did she stay here long?’ inquired Tommy.

‘Only the one night. She went away by the express the next morning back to London. It seemed a long way to come for one night, but of course I suppose Australian ladies don’t think anything of travelling.’

‘She is a very sporting girl,’ said Tommy, ‘always having adventures. It wasn’t here, was it, that she went out to