Copyright © University of Cambridge. All rights reserved.
'Power Mad!' printed from http://nrich.maths.org/
Why do this problem?
We like to offer students plenty of opportunities to work
mathematically. This problem requires students to analyse patterns,
make some generalisations, pose their own questions and explain
their findings - all key aspects of good mathematical
The first few questions are intended to highlight the impact of the
units digits on the product of two or more numbers.
On the board, write and ask for solutions to
12 x 23
42 x 73
652 x 9883
17852 x 35703
"What do all the solutions have in common?"
"What can you tell me about the product of 543789542 and
Offer the first couple of problems, give students some time to
think about them and then share their convincing arguments. Ensure
that the significance of the units digit is well understood.
Ask them to work on the next five problems and emphasise the need
to provide convincing arguments. This is ideal for a paired
"We have discovered that powers of numbers do behave in surprising
ways - can you find any other unexpected results?" Ask the students
to contribute to a whole class display of their results and their
What patterns can you find in the units digit of ascending
powers of 2, 3, 4...?
How can you be sure the patterns will continue?
This is an open ended activity which already offers plenty of
opportunities for extension work.
You might suggest that students draw up 'power tables' so that the
cyclical nature of the units digits becomes apparent.