Place four pebbles on the sand in the form of a square. Keep adding
as few pebbles as necessary to double the area. How many extra
pebbles are added each time?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Investigate the different shaped bracelets you could make from 18
different spherical beads. How do they compare if you use 24 beads?
Tobi's solution is given
To find the smallest number of crossings, put 2 sticks going
down and 8 sticks across so there will be 16.
To find the biggest number of crossings for an odd amount,
instead of splitting the sticks in half split them into the the
closest numbers to half (e.g 7 and 8).
To find the smallest number of crossings do the same as you did
before, put 2 going down and the rest going across.
Estimate for 50 sticks:
For the smallest amount put 2 down and the rest across
Estimate for any number:
To find the biggest for any number, split the amount in half and
put half across and half down but if its an odd amount split the
amount into the 2 numbers closest to half.
To find the smallest amount put 2 down and all the rest
Charles explains how to find the greatest
number of crossings for an odd number of sticks a different