## Three-Cubed Cube Puzzle

Source: Pixabay.com

**Type:** Investigation

**Theme:** Puzzles and Games

**Grades:** 7, 8, 9, 10, 11, 12

**Learning Target:** Students will build a puzzle from 27 wood cubes focusing on how to create a challenging puzzle.

Instructions

This project is for individuals.

- Criteria:
- Build a 3x3x3 cube of 1 centimeter or 1 inch wooden cubes.
- Number of cubes per puzzle piece must be no less than 4 and no greater than 6.
- Combined pieces should not construct a flat plane.

- Build your puzzle. Use only one small drop of wood glue per connection. Do not over-glue or your puzzle with not disassemble.
- Wipe off any extra glue. Let dry for a few minutes.
- Use painters tape to clamp your puzzle together as a cube.
- Let dry.
- Disassemble carefully. Use a utility knife if necessary. Re-glue any pieces that fall off in the process.
- Use a stopwatch to time six classmates for solving your puzzle. Create a histogram of the timings.

### Submission

- Photographs of your puzzle:
- Disassembled
- Solved

- Histogram of solve times.
- Questions:
- What makes a 3x3x3 block puzzle challenging?
- What steps could you take to determine all the different ways to construct a 4- to 6-cube piece?
- What does the histogram tell you about your puzzle?

### Alternative

Create a flat puzzle out of wood equilateral triangles.

Model the puzzle first using Desmos.

Exit Ticket

How many ways are there to construct a 4- to 6-cube piece? Can you write an equation to make that calculation?

CCSS Math Practice

- I can make sense of problems and persevere in solving them.

NGSS Crosscutting Concepts