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

M, M and M

Age 11 to 14
Challenge Level Yellow star
Secondary curriculum
  • Problem
  • Getting Started
  • Student Solutions
  • Teachers' Resources


Try arranging all sets of numbers in order, smallest to biggest. Which of the five positions are the easiest to fill in?
If you can think of lots of possible values for one space, try to figure out the highest and the lowest it could be, and whether there are any other conditions...

Which spaces can you fill straight away?

 

Related Collections

  • Finding all solutions (Teacher)
  • Finding all solutions (Teacher)
  • Finding all solutions
  • Working Systematically - Lower Secondary

You may also like

Bat Wings

Two students collected some data on the wingspan of bats, but each lost a measurement. Can you find the missing information?

Kate's Date

When Kate ate a giant date, the average weight of the dates decreased. What was the weight of the date that Kate ate?

Balancing the Books

How many visitors does a tourist attraction need next week in order to break even?

  • 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