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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?

Month Mania

Age 5 to 11 Challenge Level:

John from St. Edburg's wrote;

TOP LEFT
I made the numbers into a triangle, starting in the top corner. When I got to the bottom I started again at the top. I noticed that the middle row and the middle column both added up to $75$.
TOP RIGHT
I wondered what would happen if I went down, then up, then down again in a zigzag instead of just filling in the numbers downwards. I had no idea that the middle row and the middle column were going to add up to $75$ again!
BOTTOM LEFT and BOTTOM RIGHT
I tried putting the numbers in a different order again, starting in the bottom left hand corner. In the bottom left picture I did the same zigzag as in the top right, and in the bottom right picture the numbers are filled in diagonally from top to bottom. I wondered if the middle row and middle column would add up to $75$ again, but they didn't. They all added up to $70$!
Sol
When I put the numbers into this grid, I spotted that on diagonal rows the units repeat. This is because each number down the diagonals is $5$ higher than the one before it ($1, 6, 11, 16$ and $13, 18, 23, 28$).
Sol2

Well done this was really a good investigation for you - keep going !