A moment later Rupert appeared, too, clutching two plastic beakers of something steaming hot, trying to wave at Celeste and splashing half of one beaker down his coat. Max glanced around for Marguerite, but her friend was well hidden.

Strange, Max thought as she trotted after her quarry, that everyone was together on this unimportant patch of grass. If most of them were innocent bystanders, why were they all drawn to each other like that? She had the uneasy sensation that they were all being knotted together, in ways she couldn’t see. But she would see, in the end, she was sure. She slipped her detective’s notebook carefully back into her pocket.

They hadn’t gone far when Ester and Klaus arrived at a round building coated in butter-yellow paint, iced with looping white stone, like an enormous birthday cake. Max didn’t need any clever tricks to get inside this one. The double doors were wide open.

Inside was a large entrance hall with a black-and-white marble floor. In here, Ester’s click-click-click was hugely magnified, and Klaus’s footsteps sounded more enormous than ever. Max hovered at the door as the two of them went over to a woman behind a glass screen and paid her some forints. Then they disappeared through another set of double doors.

Max hurried over to the woman. A sign said Széchenyi, followed by a list of mysterious words and prices, but that didn’t really help. So Max just put down the largest forint note she had, and smiled hopefully. When smiling hopefully got no response, she tried holding up one finger. “Um,” she said, “one, please?”

This did the trick. The woman pushed back a mountain of change, and a blue plastic wristband. “Úszóruha?” she asked – and pointed at a rack of swimming costumes to her right.

This didn’t seem like a swimming pool. It was much too grand. But Max thought she had better have one, for whatever-it-was, if that was the done thing. She picked out one in strawberry red, remembered she was a secret detective, and changed it for a more forgettable navy. She pushed the change-mountain back to the woman again, who rolled her eyes, took a single coin off the top, and pushed it back. Then the woman handed Max a thick white towel, and waved her away at last. Max went through the double doors.