### 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.

### Stairs

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

### Taking a Die for a Walk

Investigate the numbers that come up on a die as you roll it in the direction of north, south, east and west, without going over the path it's already made.

# Month Mania

##### Stage: 1 and 2 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 $70$!

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 $13, 18, 23, 28$).

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