**T****he Main Challenge**

When a certain 4-digit number is **multiplied by 4**, its digits appear in reverse order. It also has both of these properties:

- its first digit is a quarter of the last one, and
- its second digit is one less than the first.

What number must it be?

**The 7puzzle Challenge**

The playing board of **the 7puzzle game** is a 7-by-7 grid containing 49 different numbers, ranging from **2 **up to **84**.

The 2nd & 6th rows contain the following fourteen numbers:

5 8 12 17 18 20 28 33 48 49 55 56 63 64

List four pairs of numbers that have a difference of 7.

**The Lagrange Challenge**

*Lagrange’s Four-Square Theorem* states that every positive integer can be made by adding up to four square numbers.

For example, **7** can be made by **2²+1²+1²+1²** (or 4+1+1+1).

There are THREE ways of making **41 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **2**, **6** and **11 **once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

1 8 25 64 125

#*CubeNumbers*

**The Target Challenge**

Can you arrive at **41** by inserting **3**, **5**, **7** and **9** into the gaps on each line?

- ◯×◯+◯–◯ = 41
- (◯+◯)×◯–◯ = 41
- (◯–◯)×◯+◯ = 41