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Exploring Wild & Wonderful Number Patterns

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?


Age 7 to 11
Challenge Level

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.