Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
Madeleine and Luke at Greystoke Primary worked
carefully on four buttons:
Jordan from Birds Bush Primary gave some
helpful detail about how we can make sure we don't miss any
Children from La Mare De Carteret
Primary school agreed with 24 being the total number of ways for
I like the way you decided you didn't
need to work out the number of ways for each button being first as
it would be the same for all buttons. Noticing short-cuts
like that is a great skill for a mathematician.
Ella who goes to North Molton Primary
looked at the number of ways to do up the buttons in a more general
way. Here is what she wrote:
Very well noticed, Ella. Dan and G
from St Saviour's also suggested this was a good way to calculate
the number of ways.
William from North Molton looked at it
slightly differently. He said:
Krystof from Uhelny Trh in Prague
used a special symbol to write this down:
Krystof explained, therefore, that for
$n$ buttons there would be $n!$ different ways of buttoning them
Alex from Maidstone Grammar expressed the
total number of ways of doing up a button slightly differently
I wonder whether you can see how these
different methods of expressing the total number of ways of doing
up the buttons are connected? If I used Alex's or Krystof's
or William's or Ella's method, would I get the same answer, say for
$10$ buttons? Why?
Well done to you all.