### 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?

# Diagonal in a Spiral

##### Stage: 2 Challenge Level:

This is the start of a spiral, starting with 1 and then moving clockwise.
For this challenge we're interested in the upper-left to lower-right diagonal, shown in green. Here is the starting example:

#### Challenge 1

Find the numbers that would be in this green upper-left to lower-right diagonal for a spiral going up to 144 instead of just 16.

#### Challenge 2

The small example above shows 7, 1, 3, 13 as the diagonal.
Now that you have a bigger diagonal going beyond 100 you need to deal with all the numbers in that diagonal in order from upper-left to lower-right.
You'll need to add the diagonal numbers in threes in order as they move through the square.
In the small example it would be 7 + 1 + 3 = 11 and 1 + 3 + 13 = 17. So your new numbers would be 11 and 17.
The totals you get for each three will give you a new set of numbers to use for Challenge 3.

#### Challenge 3a

You now need to use the numbers you got from adding the diagonal up in threes.
Use these numbers to make a total that has a 2 as the ones digit. You can only use a number once in any addition.
Do this in as many different ways as possible.

#### Challenge 3b

Do the same as in Challenge 3a but now the ones digit has to be an 8.
How many different ways are possible?