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

Inspector Morse

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

You may like to read the article on Morse code before attempting this question.

Morse Code
A
B
C
D
E
F
G
H
I
J
K
L
M
.-
-...
-.-.
-..
.
..-.
--.
....
..
.---
-.-
.-..
--
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-.
---
.--.
--.-
.-.
...
-
..-
...-
.--
-..-
-.--
--..

Translate the following message into Morse code:

Codes and hidden meanings

If each dit (dot) takes 1 unit of time, a dah (dash) 3 units of time, the pause between letters 3 units and the pause between words 7 units, how long will it take to send this message?

Samuel Morse gave E the symbol with the shortest time value (1dit) because he thought it was the most commonly used letter. I, apparently the next most common letter, uses two dits to represent it. However, the letter analysis was done over 150 years ago and language does change and, of course, it may be entirely different in different languages.

So, might there be a better allocation of symbols today?

To tackle this question try counting the number of times each letter occurs in the article on Morse Code and suggest an alternative coding based on the frequency of each letter (this is called frequency analysis).

Would it take less time to send the message above with your code than with Morse Code? To help you there is a list of the symbols and their time in the hints.

On average would you expect your code to take less time to send a message than the international Morse Code? Could there be a more efficient coding? You might also like to look at the letter frequency graph shown in Claire Ellis' article on Codes.

Of course there is always the problem of whether the style of writing you might use to send a message is the same as that of the article. In fact, if Morse were used today I think it would most likely resemble texting.

You may also like

Winning Team

Nine cross country runners compete in a team competition in which there are three matches. If you were a judge how would you decide who would win?

History of Morse

This short article gives an outline of the origins of Morse code and its inventor and how the frequency of letters is reflected in the code they were given.

Litov's Mean Value Theorem

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

  • 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