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The sight of a huge mobile caravan drawn up in the side street next to the club, obviously, from Nick’s careful study, an incident room, was unnerving and confirmation enough that it had been murder. That made his summons back here with Les all the more daunting. Curiosity fought with fear of the “fix it on anyone” approach so beloved by the police in his reading material. Even spider-catching in Antarctica suddenly seemed preferable.

“Ah, our young detective.” Bishop greeted him from one corner of the kitchen made available for a table and chairs. “You’ll be pleased to hear you can go.”

“But that’s a scene of crimes’ van outside, isn’t it?” Nick was taken aback.

“Must be the CIA.”

Nick lingered as Les hastily cleared up and left. “You mean she wasn’t poisoned?” He tried not to sound disappointed.

“She was, but we’ve cleared your food.”

“So it was the drink?”

“It was. Forensic had a sleepless night. Nothing in the bottle, nothing in any of the glasses – save the one nearest to the lady, which was bung full of cyanide. And before you say suicide, forensic have found no traces of crystals in her clothing or handbag.”

Nick bade a silent last farewell to poisoned darts. “Suppose one of the strippers poisoned one of the extra three glasses on the bar and took that with him over to the piano, instead of the one he’d first drunk from?”

“Ashamed of you, lad. Where did he keep the crystals? And there’d be a fifth glass on the piano.”

“The hat?” Nick asked without much hope.

“Forget about hats. They were clean, too. What is it every self-respecting amateur detective pounces on?”

Nick didn’t like being mocked. “Fingerprints.”

“Right. And that’s why Mr Paul Duncan is at the station helping with enquiries.”

“All the glasses would have Hamish Scott’s prints on.” Nick was thinking it through. “So if he were the murderer he wouldn’t need to worry about his prints being on Greta’s glass, but the others would.”

“Greta’s glass had Duncan’s prints on it as well as her own and Scott’s. If we could find how he transported the poison, we could wrap this up. Now, you’ve quite a name at Scotland Yard, so you think about it.”

“I’ve never even had a caution.” What the hell was this?

“I went there to the Black Museum a while ago. Back in the dark ages there was an Auguste Didier who helped Rose of the Yard in a few cases, generally those with fancy touches in them. Any relation?”

“Great-grandfather,” Nick muttered reluctantly. Too much eagerness to claim kinship might not go down too well, and in any case he wasn’t sure the news was welcome. True, an amateur detective in deepest Muckshire as a rival was way outclassed by one working with Scotland Yard. Maybe he’d check into it sometime.

“Just in case you have plans to follow in great-grandad’s footsteps, I solve my own cases. Plain and fancy. Right?”

“Right,” Nick hastily agreed.

“I don’t see how Paul Duncan can be guilty,” Nick proclaimed. Thinking of the impossible murder took his mind off his surroundings. Les’s kitchen in the rented industrial unit lurched its way through every food inspection, surviving more by luck of timing than merit.

“I told you to make that with huss.” Les peered peevishly at Nick’s work.

“For a monkfish kebab?”

“Who’s going to notice? It all gets charred to a cinder on the barbi.”

“All the Berties hated her, but they all stayed.”

“Ah, well, it was a living of some sort, even if Greta and good old Tony kept sixty per cent of it, and went on deluding them that they were building up a fund so that they could finance a launch into the big time. Not nice of Greta. It’s cheating,” Les added virtuously. He removed a chunk of fish from the end of each kebab. “Give ’em room to breathe,” he explained casually.

“No one came up from the rear, but what about from that side room on stage? The owner and his lighting chap were there. Of course, they still had to get the poison onto the stage.”

Les decided to be helpful. “You said it had to have been added between the two guzzling bouts. How about just stretching out from the wings?”

“Someone would have noticed a five-foot arm,” Nick retorted scathingly.

Les expired with a final shot. “Maybe it dropped from the ceiling. Now, could you condescend to earn some of that fortune I pay you?”

Nick did not reply. Les had set off a train of thought. He remembered Sherlock Holmes and the snake gliding down the bellrope; he remembered Dorothy Sayers, and an ingenious contraption; he even remembered poisoned darts…

“You again? Solved it yet?”

“I wondered if you’d checked the wings,” Nick blurted out, none too sure of his ground once faced with Bishop.

An amiable, if sardonic, smile. “Be my guest. Check ’em yourself. Let me know if I’ve missed anything. And let me tell you, Commander Bond, we’ve checked the spotlights and curtains half a dozen times. No cyanide crystals were showered down by guided missile, and no curtain rods left their moorings to deposit any either. Nor did anyone shoot a dart at her and poison the glass as a blind, or paint cyanide onto the piano keys so it would get absorbed into her fingers – but you didn’t think of that one.”

“No,” Nick admitted. “But the hats-”

Bishop smote his forehead. “Of course!” he cried. “Whyever didn’t you mention hats before?”

Nick ploughed doggedly on. “When the Berties stood at the piano nude, the last thing to go was the hats. Suppose the poison was held inside the brim and the murderer simply waved the hat low over the glass, released the poison somehow, then threw the hat offstage where it was switched for an identical unadulterated one.”

“Collusion? The owner will be pleased. You go and practise releasing cyanide crystals from a secret compartment on your head, as you jig up and down starkers. When you’ve succeeded, I’ll take you seriously.”

Nick subsided, crestfallen.

“If you can tell me how Paul Duncan did it – and I’m sure he did – I’ll stick a testimonial to you in the Black Museum,” Bishop said more kindly, “next to your ancestor. Remember, all these weird and wonderful ways you’ve doubtless read about in fiction didn’t have to pass the scrutiny of a couple of hundred screaming women – not to mention Mr Nick Didier’s. However glued they were to the attractions of the Berties’ persons, someone was going to see if poison shot down from the spotlights, just as they’d have noticed if any of the trio went fishing around in their fancy togs for a few cyanide crystals. Paul Duncan claims that he picked up Greta’s glass by accident; if he’s right, how did the poison get into his glass? I may be eating my own words, but perhaps this really is an impossible murder.”

“And I’ll eat my hat if it is,” Nick vowed silently.

If you eliminate the impossible, the improbable must be true, Nick told himself. It was an old-established principle in detective fiction. Only what was the improbable? If it was impossible for anyone on the stage to have carried out the murder, and the wings and ceiling had been ruled out, that left the audience – which had also been ruled out. Anyone walking up to her would have been noticed, and her husband who was closest was devoted to her. Even if that were a sham, Nick would undoubtedly have seen him, even at the critical moment of the strip, since he was tall enough for the full spotlight on the piano to pick him up if he approached his wife, and surely the women next to him and behind him would have noticed if he’d moved, even in the darkness.