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

Dart Target

Age 7 to 11
Challenge Level Yellow starYellow starYellow star
  • Problem
  • Student Solutions
  • Teachers' Resources
We have two different targets and a set of three darts.

 

You use three darts for each game.  All the darts always hit the target.


An Important Rule:-
You can only have one dart in the same coloured area on any one target, but you could, for example, have a dart in red 3 on the left target and another dart in red 3 on the right target.


CHALLENGE 1


Each time you have a game, you add up the score of the three darts.
Your challenge is to have four games each with the same total score, but made in different ways.

However, note that 1 and 2 on the left target and 3 on the right target is the same as 1 on the left target and 2 and 3 on the right target, so is counted as just one solution.


CHALLENGE 2


Have three games. The three totals must give three consecutive numbers.
In the nine darts used no number must occur more than twice.
So, when Raj chooses: 

Game 1:     2 + 3 + 4 =  9
Game 2:     1 + 4 + 5 = 10
Game 3:     1 + 5 + 5 = 11  

This is NOT allowed as three 5s have been used and the maximum is two.


CHALLENGE 3


You now move on to having three targets with four darts for each game.
As before you can only have one dart in any coloured sector of a target.

The targets are:
1, 2, 3  
1, 2, 3, 4  
1, 2, 3, 4, 5.

Firstly see how many different totals you can make.

Finally find all the ways of getting the set of three consecutive 11, 12, 13 

But in a set of three answers you must not use the same number more than three times.

So, when Sara chooses:

Game 1   1 + 2 + 3 + 5 =  11
Game 2   1 + 2 + 4 + 5  = 12
Game 3   2 + 2 + 4 + 5 =  13  

This is not allowed as four 2s have been used and the maximum is three.

Find as many answers as you can.

You may also like

Prompt Cards

These two group activities use mathematical reasoning - one is numerical, one geometric.

Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

  • 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