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 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 dine with some friends, went for a drive in their car afterwards, ran the car into a ditch and wasn't able to get home till morning?"

"Oh, no," said the young lady. "Miss Drake had dinner here in the Hotel."

"Really," said Tommy, "are you sure of that? I mean-how do you know?"

"Oh, I saw her."

"I asked because I understood she was dining with some friends in Torquay," explained Tommy.

"Oh, no sir, she dined here." The young lady laughed and blushed a little. "I remember she had on a most sweetly pretty frock. One of those new flowered chiffons all over pansies."

"Tuppence, this tears it," said Tommy when they had been shown upstairs to their room.

"It does rather," said Tuppence. "Of course that woman may be mistaken. We will ask the waiter at dinner. There can't be very many people here just at this time of year."

This time it was Tuppence who opened the attack.

"Can you tell me if a friend of mine was here last Tuesday?" she asked the waiter with an engaging smile. "A Miss Drake, wearing a frock all over pansies I believe." She produced a photograph. "This lady."

The waiter broke into immediate smiles of recognition.

"Yes, yes, Miss Drake. I remember her very well. She told me she came from Australia."

"She dined here?"

"Yes. It was last Tuesday. She asked me if there was anything to do afterwards in the town."

"Yes?"

"I told her the theatre, the Pavilion, but in the end she decided not to go and she stayed here listening to our orchestra."

"Oh damn," said Tommy under his breath.

"You don't remember what time she had dinner, do you?" said Tuppence.

"She came down a little late. It must have been about eight o'clock."

"Damn, Blast, and Curse," said Tuppence as she and Tommy left the dining-room. "Tommy, this is all going wrong. It seemed so clear and lovely."

"Well, I suppose we ought to have known it wouldn't all be plain sailing."

"Is there any train she could have taken after that I wonder?"

"Not one that would have landed her in London in time to go to the Savoy."

"Well," said Tuppence, "as a last hope I am going to talk to the chambermaid. Una Drake had a room on the same floor as ours."

The chambermaid was a voluble and informative woman. Yes, she remembered the young lady quite well. That was her picture right enough. A very nice young lady, very merry and talkative. Had told her a lot about Australia and the kangaroos.

The young lady rang the bell about half past nine and asked for her bottle to be filled and put in her bed and also to be called the next morning at half past seven-with coffee instead of tea.

"You did call her and she was in bed?" asked Tuppence,

The chambermaid stared at her.

"Why, yes Ma'am, of course."

"Oh, I only wondered if she was doing exercises or anything," said Tuppence, wildly. "So many people do in the early morning."

"Well, that seems cast iron enough," said Tommy, when the chambermaid had departed. "There is only one conclusion to be drawn from it. It is the London side of the thing that must be faked."

"Mr. le Marchant must be a more accomplished liar than we thought," said Tuppence.

"We have a way of checking his statements," said Tommy. "He said there were people sitting at the next table whom Una knew slightly. What was their name-Oglander, that was it. We must hunt up these Oglanders and we ought also to make inquiries at Miss Drake's flat in Clarges Street."

The following morning they paid their bill and departed somewhat crestfallen.

Hunting out the Oglanders was fairly easy with the aid of the telephone book. Tuppence this time took the offensive and assumed the character of a representative of a new illustrated paper. She called on Mrs. Oglander asking for a few details of their "smart" supper party at the Savoy on Tuesday evening. These details Mrs. Oglander was only too willing to supply. Just as she was leaving Tuppence added carelessly: "Let me see, wasn't Miss Una Drake sitting at the table next you? Is it really true that she is engaged to the Duke of Perth? You know her, of course."

"I know her slightly," said Mrs. Oglander. "A very charming girl I believe. Yes, she was sitting at the next table to ours with Mr. le Marchant. My girls know her better than I do."

Tuppence's next port of call was the flat in Clarges Street.

Here she was greeted by Miss Mariory Leicester, the friend with whom Miss Drake shared a flat.

"Do tell me what all this is about?" asked Miss Leicester plaintively. "Una has some deep game on and I don't know what it is. Of course she slept here on Tuesday night."

"Did you see her when she came in?"

"No, I had gone to bed. She has got her own latch key, of course. She came in about one o'clock, I believe."

"When did you see her?"

"Oh, the next morning about nine-or perhaps it was nearer ten."

As Tuppence left the flat she almost collided with a tall, gaunt female who was entering.

"Excuse me, Miss, I'm sure," said the gaunt female.

"Do you work here?" asked Tuppence.

"Yes, Miss, I come daily."

"What time do you get here in the morning?"

"Nine o'clock is my time, Miss."

Tuppence slipped a hurried half crown into the gaunt female's hand.

"Was Miss Drake here last Tuesday morning when you arrived?"

"Why yes, Miss, indeed she was. Fast asleep in her bed and hardly woke up when I brought her in her tea."

"Oh, thank you," said Tuppence and went disconsolately down the stairs.

She had arranged to meet Tommy for lunch in a small Restaurant in Soho and there they compared notes.

"I have seen that fellow, Rice. It is quite true he did see Una Drake in the distance at Torquay."

"Well," said Tuppence, "we have checked these alibis all right. Here, give me a bit of paper and a pencil, Tommy. Let us put it down neatly like all detectives do."

1.30 Una Drake seen in Luncheon Car of train.

4 o'clock Arrives at Castle Hotel.

5 o'clock Seen by Mr. Rice.

8 o'clock Seen dining at Hotel.

9.30 Asks for hot water bottle.

11:30 Seen at Savoy with Mr. le Marchant.

7.30a.m. Called by chambermaid at Castle Hotel.

9 o'clock Called by charwoman at flat at Clarges Street.

They looked at each other.

"Well, it looks to me as if Blunt's Brilliant Detectives are beat," said Tommy.

"Oh, we mustn't give up," said Tuppence. "Somebody must be lying!"

"The queer thing is that it strikes me nobody was lying. They all seemed perfectly truthful and straightforward."

"Yet there must be a flaw. We know there is. I think of all sorts of things like private aeroplanes but that doesn't really get us any forwarder."

"I am inclined to the theory of an astral body."

"Well," said Tuppence, "the only thing to do is to sleep on it. Your subconscious works in your sleep."

"H'm," said Tommy. "If your subconscious provides you with a perfectly good answer to this riddle by tomorrow morning, I take off my hat to it."

They were very silent all that evening. Again and again Tuppence reverted to the paper of times. She wrote things on bits of paper. She murmured to herself, she sought perplexedly through Rail Guides. But in the end they both rose to go to bed with no faint glimmer of light on the problem.

"This is very disheartening," said Tommy.

"One of the most miserable evenings I have ever spent," said Tuppence.

"We ought to have gone to a Music Hall," said Tommy. "A few good jokes about mothers-in-law and twins and bottles of beer would have done us no end of good."

"No, you will see this concentration will work in the end," said Tuppence. "How busy our subconscious will have to be in the next eight hours!" And on this hopeful note they went to bed.

"Well," said Tommy next morning, "has the subconscious worked?"

"I have got an idea," said Tuppence.

"You have. What sort of an idea?"

"Well, rather a funny idea. Not at all like anything I have ever read in detective stories. As a matter of fact it is an idea that you put into my head."

"Then it must be a good idea," said Tommy firmly. "Come on, Tuppence, out with it."

"I shall have to send a cable to verify it," said Tuppence. "No, I am not going to tell you. It's a perfectly wild idea but it's the only thing that fits the facts."

"Well," said Tommy, "I must away to the office. A roomful of disappointed clients must not wait in vain. I leave this case in the hands of my promising subordinate."

Tuppence nodded cheerfully.

She did not put in an appearance at the office all day. When Tommy returned that evening about half past five it was to find a wildly exultant Tuppence awaiting him.

"I have done it, Tommy. I have solved the mystery of the alibi. We can charge up all these half crowns and ten shilling notes and demand a substantial fee of our own from Mr. Montgomery Jones and he can go right off and collect his girl."

"What is the solution?" cried Tommy.

"A perfectly simple one," said Tuppence. "Twins."

"What do you mean?-Twins?"

"Why just that. Of course it is the only solution. I will say you put it into my head last night talking about mothers-in-law, twins, and bottles of beer. I cabled to Australia and got back the information I wanted. Una has a twin sister, Vera, who arrived in England last Monday. That is why she was able to make this bet so spontaneously. She thought it would be a frightful rag on poor Montgomery Jones. The sister went to Torquay and she stayed in London."