**T**** h****e Main Challenge**

List the FIVE 2-digit numbers to have the following attributes:

- are not odd numbers,
- are not multiples of 3, 4, or 7,
- has its digits adding up to more than 10.

**T****he**** 7puzzle Challenge**

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

The 1st & 5th rows contain the following fourteen numbers:

2 6 7 9 14 15 16 21 22 40 50 72 81 84

What is the sum of the factors of 36 listed above?

**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 FIVE ways of making **52 **when using *Lagrange’s Theorem*. Can you find them all?

**The Mathematically Possible Challenge**

Using **8**, **9** and **10 **once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

60 61 62 63 64 65 66 67 68 69

#*NumbersIn60s*

**The Target Challenge**

Can you arrive at **52** by inserting **4**, **6**, **8** and **9** into the gaps on each line?

- ◯×◯–◯÷◯ = 52
- ◯²–(◯+√◯×√◯) = 52
- ◯²+◯×(◯–◯)² = 52
- (√◯×◯+◯)×√◯ = 52

**A****nswers **can be found **here**.

**Click Paul Godding for details of online maths tuition.**