congenial, and they formed a pleasant little circle in the library, to drink their tea.
“Sorry I’m late,” said a cheery voice, and Philip Van Reypen joined them.
“Oh! how do you do?” cried Patty, jumping up to greet him. “Miss Farley, may I present Mr. Van Reypen? I think the rest are all acquainted.”
There were general greetings all round, and then Philip took his place with the rest.
“My aunt is here,” he said, to Patty. “A little later, perhaps, she wants to meet Miss Farley.”
“So she shall,” said Patty, remembering Miss Van Reypen’s offer to help Christine in some way. “Will you have tea?”
“Will I have tea?” echoed Philip. “That’s exactly what I’m here for. Please, yes.”
“Then here you are,” said Patty, handing him a cup; “and, incidentally, do you know how a bookworm goes through a book?”
“Ugh! what an unpleasant subject,” said Elise, with a shrug of her shoulders. “Patty, do talk of something else.”
“I can’t,” said Patty, solemnly; “I must know about the manners and customs of a well-conducted bookworm.”
“Do you mean a real bookworm, or a studious person?” asked Mr. Hepworth, who often took Patty’s questions very seriously.
“I mean the – the entomological sort,” said Patty, “and I’m in dead earnest. Who knows anything about the bookworms that really destroy books?”
“I do,” announced Kenneth, “but nothing would induce me to tell. Theirs is a secret history, and not to be made known to a curious world.”
“Pooh!” said Roger, “that’s all bluff. Patty, he doesn’t really know anything about the beasts. Now, I do. A bookworm is a grub.”
“No,” said Philip, “the book is the bookworm’s grub. And pretty dry fodder he must often find it.”
“I know what you’re going to do, Patty,” said Kenneth, in an aggrieved voice; “you’re going to set up a pair of pet bookworms in place of Darby and Juliet. Please understand that I am distinctly offended, and I prophesy that your new pets won’t be half as interesting as the goldfish.”
“Wrong again, Ken,” returned Patty; “no new pets could ever be so dear to my heart as those sweet, lovely goldfish. But, if you people don’t tell me about bookworms, I’ll have to look in the Encyclopædia; and, if there’s anything I do hate, it’s that. Christine, aren’t you up on bookworms?”
“No,” said Christine, in a shy whisper. She couldn’t yet become accustomed to the quick repartee and merry nonsense of these Northern young people.
“I used to have a pet bookworm,” began Roger, “but he got into a cook-book and died of dyspepsia.”
“Tell us what it’s all about, Patty?” said Mr. Hepworth, seeing she was really serious in her questioning.
“Why, it’s a puzzle, – a sort of conundrum. This is it. Suppose a history in three volumes is placed upon a bookshelf. Suppose each volume contains just one hundred pages. And suppose a bookworm, starting at page one of volume one, bores right straight through the books, covers and all, to the last page of volume three. How many leaves does he go through, not counting fly-leaves, or covers?”
“Patty, I’m surprised at you,” said Roger. “That’s too easy. He goes through the three hundred pages, of course.”
“It does seem so,” said Patty, with a perplexed look, “but, as you say, that’s too easy. There must be a catch or a quibble somewhere.”
“Well,” said Elise, “I never could do a puzzle. I don’t know why a hen goes across the road, or when is a door not a door. But you’re a born puzzlist, Patty, and, if you can’t guess it, nobody can.”
“Elise, you’re a sweet thing, and most complimentary. But I know you have no talent for puzzles, so, my dear child, I’m not asking you. But, you men of brains and intellect, can’t you help me out? I’m sure there’s another answer, but I can’t think what it would be.”
“Why, Patty,” said Mr. Hepworth, thoughtfully, “I think Roger is right. If the bookworm goes through all three volumes, he must go through three hundred pages, mustn’t he?”
“No, indeed!” cried Christine, her shyness forgotten, and her eyes shining as she constructed the picture of the books in her mind’s eye. “Wait a minute; yes, I’m sure I’m right! He only goes through one hundred pages. He goes only through the second volume, you see!”
Elise looked at Christine a little disdainfully.
“You don’t seem to have heard the conditions,” she said. “The bookworm begins at the first page of the first volume and goes through to the end of the last one.”
“Yes, I heard that,” said Christine, flushing at Elise’s tone, which was distinctly supercilious. “But, don’t you see, when the books are set up on a shelf, in the usual manner, the first page of the first volume is on the right, just up against the last page of the second volume.”
“Nonsense!” cried Elise.
“But it is so, Miss Farley!” exclaimed Philip Van Reypen. “You’ve struck it! Look, people!”
He turned to a bookcase, and indicated three volumes of a set of books.
“Now, see, the first page of volume one is right against the last page of volume two. So the first page of volume two is up against the last page of volume three. Now, what does Mr. Bookworm do? He starts here, at the first page of volume one. He doesn’t go backward, so he doesn’t go through volume one at all! He goes through volume two, and, as soon as he strikes volume three, he strikes it at the last page, and his task is done, his journey is over. He has fulfilled the conditions of the original question. See?”
They did see, after awhile, but it was only the ocular demonstration that proved it, for the facts were hard to describe in words.
Elise flatly refused to see it, saying it made her head ache to try to understand it.
“But it was very clever of Miss Farley to reason it out so soon,” said Philip.
“Yes, wasn’t it?” agreed Patty. “I didn’t know you had a bent for puzzles, Christine.”
“I haven’t. But that doesn’t seem to me like a puzzle. I can’t do arithmetical problems, or guess charades at all. But this seems to me a picture of still life. I can see the insides of the books in my mind, and they are wrong end to, – that is, compared to the way we read them. You see, they really stand in the bookcase with the pages numbered backward.”
“Bravo, Christine; so they do!” said Mr. Hepworth. “Patty, that’s the answer, but, I confess, I was ’way off myself.”
“So say we all of us,” chimed in Roger. “I can only see through it, part of the time, even now.”
“I think it a most clever catch question,” said Philip Van Reypen. “Where did you find it, Miss Fairfield?”
“In a little book of puzzles; I’m trying
