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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?

Investigating Pascal's Triangle

Age 7 to 11 Challenge Level:

I think that it's time to look at Pascal's Triangle afresh. So, let's see what happens when we turn it around in a special way.
So we start with the layout as usual, turn it anticlockwise 45 degrees and then take off the top line of ones.
Turn1 Turn 2 Turn3
So the first 9 lines would look like this ;

corrected pascal
BUT if we take the digital roots of the numbers and see the first 30 lines we have a new look to Pascal's Triangle as shown below.


So here you have an awful lot of numbers in rows and columns to explore.

Those of you with some spreadsheet experience (or those of you that are quick to learn such things!) should go to the HINT at this point, before going further.

Some starting points for further explorations.

1. On my spreadsheet I decided to explore the rows that are multiples of 9 as I had noticed that there were a lot of 141's and 171's in those lines. Because that is what I wanted to explore I only wrote down the first number that comes after the patterns I was exploring [that's why there are lots of spaces in two out of every three rows.]

So you could do a similar thing, looking at line numbers of a different multiple.
If you do a few you then could compare your discoveries.

2. You could take just one line [e.g.30] and use the spreadsheet to extend it very far.
Here I've taken line 30, and grouped the numbers in that row in 9's and then three 9's together and underneath each other. I did this because my eyes led me to some interesting repetitions. I then noted down things according to the columns I had placed them under.

See what other things you can notice with this line or any other that you choose.

a) Look for additions that are interesting;
b) Look at repeats of numbers;
c) Look for reflections of patterns.

AND see if you can explainWHY? these patterns are occurring.