Allora and the Puzzles of Archimedes [PDF + eBook + Worksheets]

A 197-page fantasy novel that teaches friction, levers, pulleys, and number puzzles through the adventures of Allora, a young apprentice to Wizard Leibniz who accidentally turns off friction with a magical 2,000-year-old puzzle called the Ostomachion — and then has to fix the slippery, chaotic mess she's made. Along the way she works with Newton, Archimedes himself, a Fairy Queen, and a band of trolls.

Written by Sarah Allen, illustrated in black and white by Marie Delwart. For ages 9–12.

What's inside the book

• Fourteen chapters of fantasy adventure (roughly 185 pages) following Allora through a world where the laws of physics have been broken and need to be put back.
• "A Note from the Librarian" sidebars woven throughout, connecting the magic to real physics and math: static and kinetic friction (and the equation f = μN), Newton's Third Law, levers and mechanical advantage, pulleys, and a glimpse of Archimedes' famous cylinder-vs-sphere discovery.
• Hands-on suggestions embedded in the story — things kids can try with a spinny chair, their palms on a desk, or a real lever.
• The Ostomachion puzzle as a central plot device. (It's a real ancient puzzle attributed to Archimedes — sometimes called "the first puzzle" — and you can download a printable version free from my website to try yourself.)

Plus a bonus: Archimedes' Puzzle Book (28 pages)

A separate illustrated puzzle book with full answer key, designed to let kids practice what Allora learns:

• Lever puzzles — Which Way Will the Lever Tip? · Identify the Effort, Load, and Fulcrum · A Castle Demolition Puzzle
• Pulley puzzles — Understanding tension forces in single and compound pulley systems · "Would this actually do anything???" (figuring out which pulley contraptions provide mechanical advantage and which don't)
• A Certificate of Puzzle Mastery at the end for kids who make it through

Plus three additional worksheets (with answer keys)

Designed as a progression from intuition to calculation to puzzle-solving:

• Friction Explorer — pairs with a free interactive friction simulator on my website. Kids predict, then drag a block around, then experiment with turning static and kinetic friction on and off to see what really happens. Conceptual, no calculations.
• Calculating Friction — works through the friction equation f = μN with characters from the book, including multi-step problems where the normal force changes (a hawk lifting a chair, pushing down on a broom).
• Flower Garden Riddles — integer puzzles based on Archimedes' Cattle of the Sun problem, introducing primes, squares, triangular numbers, and Diophantine equations through trolls, fairies, dwarves, and dragons. Includes the original Greek riddle as a bonus at the back for the very ambitious.

What you'll get

• EPUB of the book (for Kindle, Apple Books, Kobo, and other e-readers)
• PDF of the book (for reading on any computer, tablet, or phone — or for printing)
• PDF of Archimedes' Puzzle Book, with answer key
• PDFs of the Friction Explorer, Calculating Friction, and Flower Garden Riddles worksheets, with answer keys
• Delivered by email immediately after purchase, plus available on your download page

Part of the Fairy Tale Physics series

Each book in the series is self-contained, so you can start anywhere. Allora's story stands on its own, though sharp-eyed readers may notice familiar faces (Newton and Leibniz, for instance, both make appearances).

About the author

Sarah Allen tutored math and physics for twenty years before becoming a full-time fantasy writer. She has a physics degree from the University of Washington (graduated with college and departmental honors) and a master's in Cognition and Learning from Columbia. Her goal is to write the sort of physics books she would have wanted as a kid.

Ages 9–12 · 197-page novel · 28-page puzzle book · 3 worksheets · Black-and-white illustrations