Lewis Carroll is famous for just one story (and its sequel, which is usually lumped in with the first), but he wrote a number of other works. They’re all worse, which explains why they aren’t as famous. But in several of them, the fun math-and-wordplay that Alice in Wonderland is known for comes through. Here’s an excerpt from A Tangled Tale, a 1885 collection of funny stories built around math puzzles, in which a little girl points out a flaw in her governess’s reasoning:
“And what made you choose the first train, Goosey?” said Mad Mathesis, as they got into the cab. “Couldn’t you count better than that?”
“I took an extreme case,” was the tearful reply. “Our excellent preceptress always says, ‘When in doubt, my dears, take an extreme case.’ And I was in doubt.”
“Does it always succeed!” her aunt inquired.
Clara sighed. “Not always,” she reluctantly admitted. “And I ca’n’t make out why. One day she was telling the little girls — they make such a noise at tea, you know — The more noise you make, the less jam you will have, and vice versa.’ And I thought they wouldn’t know what ‘vice versa’ meant: so I explained it to them. I said, ‘if you make an infinite noise, you’ll get no jam: and if you make no noise, you’ll get an infinite lot of jam.’ But our excellent preceptress said that wasn’t a good instance. Why wasn’t it?” she added plaintively.
Her aunt evaded the question. “One sees certain objections to it,” she said. “But how did you work it with the Metropolitan trains? None of them go infinitely fast, I believe.”
“I called them hares and tortoises,” Clara said — a little timidly, for she dreaded being laughed at. “And I thought there couldn’t be so many hares as tortoises on the Line: so I took an extreme case — one hare and an infinite number of tortoises.”
“An extreme case, indeed,” her aunt remarked with admirable gravity: “and a most dangerous state of things!”
“And I thought, if I went with a tortoise, there would be only one hare to meet: but if I went with the hare — you know there were crowds of tortoises!”
Here’s the rest: A Tangled Tale