Allora and the Puzzles of Archimedes [Paperback]

A 197-page black-and-white 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.

Shipping: This is a print-on-demand paperback. Please allow 2–3 weeks for printing and delivery. If you need it sooner, the paperback is also available on Amazon with faster shipping.

What's inside the book

Read a Sample

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.)

Included with your paperback: bonus digital materials

Your purchase also comes with a set of downloadable PDF extras, delivered by a separate digital-download email after you order:

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 — 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

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.

To summarize, here's everything you'll get

• The paperback novel (197 pages, black-and-white illustrations), shipped to you
• PDF of Archimedes' Puzzle Book, with answer key
• PDFs of the Friction Explorer, Calculating Friction, and Flower Garden Riddles worksheets, with answer keys
• The digital extras arrive by email after purchase; the paperback arrives in 2–3 weeks

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