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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.

Magazines

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.

Pebbles

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

You can probably see all kinds of things to explore. Those of you who are familiar with spreadsheets can extend the pattern further. You would put 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, etc across the top and then you have to add the first 1 with nothing/zero that's beneath it to get the next line started. Let me show you clearly, here's the first part of the spreadsheet I used:
2bSpreadPic
So, row 2 is simply the numerals going 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, etc.
Row 3; C3 is made from B3 + B2; D3 = C2 + C3 etc.[C3 = 1 + 0, D3 = 2 + 1 etc.]
Row 4, is made up in the same way so, D4= C3 + C4, etc.

So those formulae can be put in easily and then dragged through the other cells.
BUT we are dealing with digital roots which the computer deals with as MOD 9 [a kind of clock going from 1 to 9].

Let's have a look at the formulae that we need for the 4 cells in row 3, they are as follows,

Formula
Once you have these you can drag the formulae through more cells to the right and also down.

In this way you can extend the pattern as long as the spreadsheet will allow.

Enjoy!