"You do think you know about everything," said her husband.

"I do," said Tuppence.

"And now to examine our data," said Tommy drawing the papers towards him. "First the photograph-hm-quite a nice looking girl-and quite a good photograph I should say. Clear and easily recognizable."

"We must get some other girls' photographs," said Tuppence.

"Why?"

"They always do," said Tuppence. "You show four or five to waiters and they pick out the right one."

"Do you think they do?" said Tommy-"pick out the right one I mean."

"Well, they do in books," said Tuppence.

"It is a pity that real life is so different from fiction," said Tommy. "Now then what have we here? Yes, this is the London lot. Dined at the Bon Temps seven thirty. Went to Duke's Theatre and saw Delphiniums Blue. Counterfoil of theatre ticket enclosed. Supper at the Savoy with Mr. le Marchant. We can, I suppose, interview Mr. le Marchant."

"That tells us nothing at all," said Tuppence, "because if he is helping her to do it he naturally won't give the show away. We can wash out anything he says now."

"Well, here is the Torquay end," went on Tommy. "Twelve o'clock train from Paddington, had lunch in the Restaurant Car, receipted bill enclosed. Stayed at Castle Hotel for one night. Again receipted bill."

"I think this is all rather weak," said Tuppence. "Anyone can buy a theatre ticket, you need never go near the theatre. The girl just went to Torquay and the London thing is a fake."

"If so, it is rather a sitter for us," said Tommy. "Well, I suppose we might as well go and interview Mr. Ie Marchant."

Mr. le Marchant proved to be a breezy youth who betrayed no great surprise on seeing them.

"Una has got some little game on, hasn't she?" he asked. "You never know what that kid is up to."

"I understand, Mr. le Marchant," said Tommy, "that Miss Drake had supper with you at the Savoy last Tuesday evening."

"That's right," said Mr. le Marchant. "I know it was Tuesday because Una impressed it on me at the time and what's more she made me write it down in a little book."

With some pride he showed an entry faintly pencilled: "Having supper with Una. Savoy. Tuesday 19th."

"Where had Miss Drake been earlier in the evening? Do you know?"

"She had been to some rotten show called Pink Peonies or something like that. Absolute slosh so she told me."

"You are quite sure Miss Drake was with you that evening?"

Mr. le Marchant stared at him.

"Why, of course. Haven't I been telling you?"

"Perhaps she asked you to tell us," said Tuppence.

"Well, for a matter of fact she did say something that was rather dashed odd. She said, what was it now? 'You think you are sitting here having supper with me, Jimmy, but really, I am having supper two hundred miles away in Devonshire.' Now that was a dashed odd thing to say, don't you think so? Sort of astral body stuff. The funny thing is that a pal of mine, Dicky Rice, thought he saw her there."

"Who is this Mr. Rice?"

"Oh, just a friend of mine. He had been down in Torquay staying with an aunt. Sort of old bean who is always going to die and never does. Dicky had been down doing the dutiful nephew. He said, 'I saw that Australian girl one day-Una something or other. Wanted to go and talk to her but my aunt carried me off to chat with an old Pussy in a bathchair.' I said, 'When was this?' and he said, 'Oh, Tuesday about tea time.' I told him of course that he had made a mistake, but it was odd, wasn't it? With Una saying that about Devonshire that evening."

"Very odd," said Tommy. "Tell me, Mr. le Marchant, did anyone you know have supper near you at the Savoy?"

"Some people called Oglander were at the next table."

"Do they know Miss Drake?"

"Oh yes, they know her. They are not frightful friends or anything of that kind."

"Well, if there's nothing more you can tell us, Mr. le Marchant, I think we will wish you good morning."

"Either that chap is an extraordinary good liar," said Tommy as they reached the street, "or else he is speaking the truth."

"Yes," said Tuppence. "I have changed my opinion. I have a sort of feeling now that Una Drake was at the Savoy for supper that night."

"We will now go to the Bon Temps," said Tommy. "A little food for starving sleuths is clearly indicated. Let's just get a few girls' photographs first."

This proved rather more difficult than was expected. Turning into a photographer's and demanding a few assorted photographs, they were met with a cold rebuff.

"Why are all the things that are so easy and simple in books so difficult in real life?" wailed Tuppence. "How horribly suspicious they looked. What do you think they thought we wanted to do with the photographs? We had better go and raid Jane's flat."

Tuppence's friend Jane proved of an accommodating disposition and permitted Tuppence to rummage in a drawer and select four specimens of former friends of Jane's who had been shoved hastily in to be out of sight and mind.

Armed with this galaxy of feminine beauty they proceeded to the Bon Temps where fresh difficulties and much expense awaited them. Tommy had to get hold of each waiter in turn, tip him and then produce the assorted photographs. The result was unsatisfactory. At least three of the photographs were promising starters as having dined there last Tuesday. They then returned to the office where Tuppence immersed herself in an A.B.C.

"Paddington twelve o'clock. Torquay three thirty-five. That's the train and le Marchant's friend, Mr. Sago, or Tapioca or something, saw her there about tea time."

"We haven't checked his statement, remember," said Tommy. "If, as you said to begin with, le Marchant is a friend of Una Drake's, he may have invented this story."

"Oh, we'll hunt up Mr. Rice," said Tuppence. "I have a kind of hunch that Mr. le Marchant was speaking the truth No, what I am trying to get at now is this. Una Drake leaves London by the twelve o'clock train, possibly takes a room at a hotel and unpacks. Then she takes a train back to town arriving in time to get to the Savoy. There is one at four forty gets up to Paddington at nine ten."

"And then?" said Tommy.

"And then," said Tuppence, frowning, "it is rather more difficult. There is a midnight train from Paddington down again but she could hardly take that, that would be too early."

"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 note 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."