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

It's a Tie

Age 7 to 11
Challenge Level Yellow starYellow star
  • Problem
  • Getting Started
  • Student Solutions
  • Teachers' Resources
Kaia's father always wore a white shirt and coloured tie for work. He didn't like deciding which tie to wear so he would put his hand in the drawer and wear the first tie that he pulled out. Each evening the tie would go back in the drawer.

One Friday morning, Kaia said, "Do you like that tie? You usually wear it at least twice a week."
"I do not," replied her father, "I have eight ties and I only work five days a week. I certainly don't wear any tie more than once a week."
"You have worn that tie twice a week in at least five of the ten weeks you have been taking me to school," Kaia insisted.
"Impossible! Prove it!" challenged her father.

Do you think Kaia or her father was right? Why?

That weekend Kaia did an experiment. She made the following drawings of his ties and created the chart shown below.

eight different ties labelled A-H
Week no. Monday Tuesday Wednesday Thursday Friday
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

How might Kaia use the drawings and chart to prove her father wrong?
Try doing an experiment yourself to find out which ties might be chosen.
What did the result of your experiment show?

You may also like

Roll These Dice

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

Stop or Dare

All you need for this game is a pack of cards. While you play the game, think about strategies that will increase your chances of winning.

Game of PIG - Sixes

Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?

  • 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