“Did you not notice that one of the people in the basket is simply ‘a murderer’? That’s you, or me, if we choose to throw people out. It’s a—what do you call it?” Wolf recalled the one time Mrs. Beathag Hide had stood in for the math teacher. The children had been given a very bizarre lesson on the philosophy of unsolvable problems that had involved the question of when a group of objects becomes a heap, and a lot about pathological liars. “A paradox,” said Wolf, remembering the word. “All these problems are unsolvable paradoxes. In choosing to throw out the murderer, you actually choose to throw yourself out, but then you can’t do any more choosing. And anyway, if you think murderers are bad, then why are you so quick to actually become one?”

“I have no idea what you’re going on about,” said Lucy coldly. “But if you mess this up you may as well be throwing out me, you, my mother and your sister. So who’s the murderer now?”

“But don’t you see?” Wolf said. “These are trick questions. For example, it should be impossible to throw out the scientist who is destined to come up with a cure for cancer.”

“What do you mean?”

“Well, if he—or it could be a she, or a they, they don’t tell you—is going to come up with a cure for cancer, they’re not going to be thrown out of a balloon, are they?”

“You’re just overcomplicating it,” said Lucy. “I’m going to put in my list for both of us, then. I think I’m actually going to go for all the animals first, regardless of weight. Elephant, guide dog, kitten . . .”

“I’m not doing this,” said Wolf, shaking his head, and sitting back in his chair.

“The participants must work together,” came the voiceover.

“I’m not doing it,” said Wolf to the speaker the voice was coming from. “If you don’t like it you can eliminate me.”

When Neptune and Malvasia reached the cats’ home it was almost two o’clock in the morning. This is a time when cats are usually at their most active, prowling around gardens, fighting one another, disemboweling small mammals and leaving their innards inside their human companions’ shoes, or simply depositing live mice at strategic locations—the kitchen table, an unoccupied pillow—chosen to most impress the human, who can always be relied upon to scream in delight when such discoveries are made.

But the cats’ home was in darkness, and there were no signs of any cats at all in the grounds. Did this place—gulp—not have a cat flap? But then where did the cats . . . ? How did they . . . ?