Lewis Carroll in Numberland by Robin Wilson

Published by Allen Lane

Lewis Carroll’s “fantastical mathematical logical life” is charted from his birth in Cheshire through to his academic career at Christ Church, Oxford.  Along the way, Carroll’s mathematical puzzles and diversions are explored as well as other aspects of his life – such as his contribution to the development of photography.  We meet characters from the Alice books as well as the wide range of Carroll’s interests – from the logic puzzles and his invention of Carroll diagrams to solve them, to different methods for voting in elections.

Idea for the classroom:  Fit the Third, Three Tricks

Three number tricks are described – explore them to discover how and why they work, giving lots of practice in arithmetic and insight into the number system.

The addition sum: I asks you for a 4 digit number, eg. 2879; I then write down another number (22877) and hide it;  We take it in turns to propose 4 more numbers (eg. you say 4685, I say 5314, you say 7062, I say 2937); add the five numbers together to get the hidden total.  What numbers should I choose?

Counting alternately to 100 (a Nim-type game): start at 1 and take it in turns to add a new number from 1 to 10; the person who reaches 100 is the winner.  How can you make sure you always win?

The “9″ trick:  You choose a number, reverse it and subtract the smaller number from the larger.  Remove any digit (except 0) from the answer and tell me the sum of the remaining digits.  I can then tell you which digit you removed.  How?