Klarner Pentacube Puzzle | 25 Y-Pentacubes 3D Packing Puzzle | Advanced Mathematical Brain Teaser | STEM Logic Challenge

Think you’ve mastered packing puzzles? Think again.

The Klarner Pentacube Puzzle is one of the most famous three-dimensional packing puzzles in recreational mathematics. Your challenge is to fit 25 identical Y-shaped pentacubes into a perfect 5 × 5 × 5 cube.

Although every piece has the same shape, solving the puzzle is extraordinarily difficult. Success requires careful planning, spatial visualization, and a great deal of patience. It’s a puzzle that continues to challenge mathematicians, educators, and puzzle enthusiasts more than fifty years after it was first introduced.

Each set includes a sturdy storage box and 25 Y-shaped pentacubes, making it an impressive display piece as well as a rewarding long-term challenge.

Available Sizes

Regular

* Box: 90 × 90 × 90 mm (3.5 × 3.5 × 3.5 in)

Large

* Box: 200 × 200 × 200 mm (7.9 × 7.9 × 7.9 in)
* Approximate Weight: 2.5 kg (5.5 lb)

XLarge

* Box: 310 × 310 × 310 mm (12.2 × 12.2 × 12.2 in)
* Approximate Weight: 6.8 kg (15.0 lb)

The History Behind the Puzzle

The puzzle was inspired by the work of mathematician David A. Klarner, a pioneer in the study of polycubes and pentacubes. In 1970, Klarner and C. J. Bouwkamp published their landmark paper “Packing a Box with Y-Pentacubes,” proving that twenty-five identical Y-shaped pentacubes can completely fill a 5 × 5 × 5 cube. (⁠Eindhoven Research Portal)

Since then, the puzzle has become a classic in recreational mathematics. Despite all pieces being identical, the challenge is surprisingly deep. Modern computer analysis has shown there are 1,264 fundamentally different solutions (excluding rotations and mirror images), highlighting both the puzzle’s elegance and its remarkable complexity. (⁠Rogelio Tomas)

Features

* Complete set of 25 identical Y-shaped pentacubes
* Storage box included
* Forms a perfect 5 × 5 × 5 cube
* One of the most famous 3D packing puzzles ever created
* Exceptional challenge for experienced puzzlers
* Outstanding STEM educational resource
* Beautiful display piece when completed

Great For

* Advanced puzzle enthusiasts
* Recreational mathematicians
* STEM education
* University mathematics departments
* Teachers and classrooms
* Puzzle collectors
* Engineering students
* Spatial reasoning practice
* Unique gifts

Materials

Crafted from durable PLA plastic, a biodegradable and eco-friendly material built to withstand years of solving and display.

What’s Included

* 25 Y-shaped pentacubes
* Storage box

Difficulty: Expert

This is one of the most challenging packing puzzles in our collection and is recommended for experienced puzzle solvers looking for a truly rewarding mathematical challenge.

⸻

About ItemsByCL

ItemsByCL was built around one simple idea: every product should spark curiosity or put a smile on someone’s face.

We specialize in mathematical puzzles, brain teasers, and hands-on learning experiences that transform abstract concepts into engaging physical challenges. Many of our designs are inspired by classic recreational mathematics and are enjoyed by educators, students, collectors, and puzzle enthusiasts around the world.

Whether you’re searching for an extraordinary gift, a classroom centerpiece, or your next great puzzle challenge, our goal is to create products that inspire curiosity, creativity, and a lifelong love of problem solving.

Thank you for supporting a small business dedicated to making mathematics both beautiful and interactive.