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

Number of Arms

Age 11 to 14
ShortChallenge Level Yellow starYellow starYellow star
Secondary curriculum
  • Problem
  • Solutions

We begin by assuming that almost everybody has 2 arms. Nobody has 3, but a small number of people have lost one or both arms in accidents or amputations. Here, we will ignore fractional arms - but you don't actually have to.

Measure What it is Value More than this many arms
Mean If all of the arms in the world were shared equally between all of the people Just below 2 2
Median The middle number, when everybody's number of arms is written in a long, ordered list:
0, ..., 0, 1, ..., 1, 2, ..........................................................., 2
2 3
Mode  The most common number of arms 2 3

The next person you meet will probably have 2 arms, and definitely won't have more.

So it is almost certain that they have more than the mean number of arms, but impossible that they have more than the median or modal number of arms.




You can find more short problems, arranged by curriculum topic, in our short problems collection.

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