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

Here are seven mental arithmetic questions for you to try:

- Which number multiplied by itself gives 196?
- What is 50 + 400 + 5?
- 54 – 45 = ?
- If Jo runs 10 miles in one hour, how much further would she get in an extra 15 minutes running at the same rate?
- (14 – 3) × (7 + 2) = ?
- Which fraction comes next in the list: 1/12, 1/6, 1/4, 1/3, …
- How many days equal 6 weeks?

**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

List FIVE different numbers that total 100.

**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 SEVEN ways of making **106 **when using *Lagrange’s Theorem*. Can you find them all?

**The Mathematically Possible Challenge**

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

4 8 12 16 20 24 28 32 36 40

#*4TimesTable*

**The Target Challenge**

Can you arrive at **106** by inserting **4**, **5**, **6** and **7** into the gaps on both lines?

- ◯²+◯²+◯²+◯ = 106
- ◯³–(◯+◯)×double◯ = 106

**An****swers **can be found **here**.

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