EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Let's suppose that you are going to have a magazine which has 16
pages of A5 size. Can you find some different ways to make these
pages? Investigate the pattern for each if you number the pages.
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?
V. Rolfe sent the following very clear
solution to the Beads problem:
1) All three beads are red - RRR
When more beads are added, they will also be red as all the beads
are the same colour. The pattern therefore remains the same.
2) Three blue beads - BBB
Three red beads are added as the beads are all the same colour, we
then have the scenario described above, with three red beads and
the pattern remains red.
Thus BBB becomes RRR
3) Two blue beads and one red bead - BBR (The order is not
significant in the circle)
There are two sets of beads of different colours next to each other
therefore two blue beads are inserted. The two blue beads lead to
the insertion of one red bead.
Thus two blue beads and one red bead are added so the pattern
remains constant, although the ring does 'rotate'.
4) Two red beads and one blue bead - RRB
This is the scenario above with two different coloured beads next
to each other and one pair of the same colour. Two blue beads and
one red bead are therefore inserted. When the original beads are
removed the pattern becomes that described above, BBR.
Thank you - you have gone through the
possibilities very systematically.