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

Ante Up

Age 16 to 18
Challenge Level Yellow starYellow star
  • Problem
  • Getting Started
  • Student Solutions
  • Teachers' Resources

A computer is programmed to produce a long string of Hs and Ts which are printed out onto a piece of ticker tape which has been divided into square boxes.
 
Each time a button is pressed the tape advances by one 'unit' and the bottom box cut off, so there are always three boxes visible in a line. The number of units of paper remaining inside the machine is indicated in the circle.
 
 

 
Alan Turing, the great code breaker, and I are each given a slip which we each mark with Hs and Ts. Whoever sees their sequence emerge first from the machine wins. I choose HTT and Turing chooses HHT as shown in the diagram.
 
 
 
 
If the machine configuration is as shown in the diagram at the moment, who is more likely to win: Turing or me?

Suppose we were going to play again and Turing chooses the sequence THT. Being a bit of a spy, I find this information out before I choose my sequence. Before we play we are going to reload the machine so that it contains 6 units of paper. Can I choose a sequence which is more likely to win than Turing's?

Difficult Extension: After playing with these choices many times, Turing is fed up with losing and wants to choose TTH. He also wants to load the machine with infinitely many units of paper. Can I choose a sequence which is more likely to beat Turing's new choice?
 

You may also like

Rain or Shine

Predict future weather using the probability that tomorrow is wet given today is wet and the probability that tomorrow is wet given that today is dry.

Squash

If the score is 8-8 do I have more chance of winning if the winner is the first to reach 9 points or the first to reach 10 points?

Playing Squash

Playing squash involves lots of mathematics. This article explores the mathematics of a squash match and how a knowledge of probability could influence the choices you make.

  • 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