Skip over navigation
Cambridge University Faculty of Mathematics NRich logo
menu search
  • Teachers expand_more
    • Early years
    • Primary
    • Secondary
    • Post-16
    • Events
    • Professional development
  • Students expand_more
    • Primary
    • Secondary
    • Post-16
  • Parents expand_more
    • Early Years
    • Primary
    • Secondary
    • Post-16
  • Problem-Solving Schools
  • About NRICH expand_more
    • About us
    • Impact stories
    • Support us
    • Our funders
    • Contact us
  • search

Or search by topic

Number and algebra

  • The Number System and Place Value
  • Calculations and Numerical Methods
  • Fractions, Decimals, Percentages, Ratio and Proportion
  • Properties of Numbers
  • Patterns, Sequences and Structure
  • Algebraic expressions, equations and formulae
  • Coordinates, Functions and Graphs

Geometry and measure

  • Angles, Polygons, and Geometrical Proof
  • 3D Geometry, Shape and Space
  • Measuring and calculating with units
  • Transformations and constructions
  • Pythagoras and Trigonometry
  • Vectors and Matrices

Probability and statistics

  • Handling, Processing and Representing Data
  • Probability

Working mathematically

  • Thinking mathematically
  • Developing positive attitudes
  • Cross-curricular contexts

Advanced mathematics

  • Decision Mathematics and Combinatorics
  • Advanced Probability and Statistics
  • Mechanics
  • Calculus

For younger learners

  • Early Years Foundation Stage

Cuboid-in-a-box

Age 7 to 11
Challenge Level Yellow starYellow starYellow star
  • Problem
  • Getting Started
  • Student Solutions
  • Teachers' Resources
We have a really good box to store things in.
It's a cuboid that's 12 cm long, 8 cm wide and 10 cm high.

cube on own
We so often get asked for the biggest something or other, so for a change, here's a challenge with a difference:

What is the SMALLEST CUBOID that you can put in the box so that you cannot fit another that's the same into it?

You could use little cubes that are 1 cm wide, long and high that clip together or make a cuboid that must be a whole number of cm wide, long and high.

Let us know what you come up with - and what is more important - how you came to get a solution.


You may also like

Multilink Cubes

If you had 36 cubes, what different cuboids could you make?

Construct-o-straws

Make a cube out of straws and have a go at this practical challenge.

Cereal Packets

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

  • Tech help
  • Accessibility Statement
  • Sign up to our newsletter
  • Twitter X logo

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

University of Cambridge logo NRICH logo