### 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.

### Sending Cards

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

# 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 !