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

Gathering Gems

Age 5 to 11
Challenge Level Yellow star
  • Problem
  • Getting Started
  • Student Solutions
  • Teachers' Resources
The following solutions arrived from Peak School in Hong Kong:

Jamie:
First, I will find a way to get all the gems. Then I counted how many times I went and then if it is more than 10, I need to make it to 10 or lower. Then I will have the answer.

Cassie and HazeӬ:
How we did it was first we went West 7 times then we went East once. After that, we went North 5 times and South 1 time. Then we went East 5, North 8, West 6, South 6 and East 3 times.  
Our strategy was whenever we went too far we would go back 1 space and after our hard work, we finally made it to the end.

Guillermo:
It doesn't matter what solution you enter because it is random every time so you can never get a straight answer. So the directions I used where N5 E6 S8 W8 N1 E5 N6 W2 S4 W1 and that was the solution that got me all 20 gems and got home.

William & Evelyn:Ӭ
We tried to calculate how many moves we needed to use in order to get from the closest gem to the farthest while using as few moves as possible, while collecting as many gems on the way and still saving enough moves to get back "Home". By using this method we collected all 20 gems.

  • 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