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

Last chance to get all seven correct. Be careful as there may be one or two tricky ones!

- (1 – 2) – (3 – 4) = ?
- 4 ÷ 0.5 = ?
- What is 25 less than the product of 20 and 10?
- How do you write “Six and six hundredths” in decimal format?
- 4,000 × 0.02 = ?
- Find 10% of £13.
- What is 31 × 15?

**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 1st & 2nd rows contain the following fourteen numbers:

2 8 9 14 15 17 22 28 40 48 55 63 64 72

What is the sum of the odd numbers?

**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 **109 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **1**, **4** and **9 **once each, with + – × ÷ available, which TWO numbers is it possible to make from the list below?

7 14 21 28 35 42 49 56 63 70

#*7TimesTable*

**The Target Challenge**

Can you arrive at **109** by inserting **3**, **8**, **10** and **12** into the gaps on both lines?

- ◯×◯–(◯+◯) = 109
- ◯×◯+◯+◯ = 109

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

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