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

Here’s another selection of mental arithmetic questions. Can you answer all seven correctly?

- (10 + 10) – (15 – 3) = ?
- What is the sum of 0.83 and 0.89?
- What is 1 × 9?
- If Ben earns £10 every half-hour, how much will he earn in 40 hours?
- If you burn 100 calories by climbing 100 stairs, how many calories would you burn when climbing 50 stairs?
- What is 5,456 – 4,372?
- Twice my age plus 4 more is 72. How old am I?

**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 & 5th rows contain the following fourteen numbers:

6 7 8 16 17 21 28 48 50 55 63 64 81 84

What is the product of the two prime 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 just THREE ways of making **104 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **5**, **7** and **10 **once each, with + – × ÷ available, which are the only TWO numbers it is NOT possible to make from the list below?

25 35 45 55 65 75 85 95 105 115

#*MultiplesOf5*

**The Target Challenge**

Can you arrive at **104** by inserting **2**, **4**, **12** and **15** into the gaps on both lines?

- (◯–◯)×(◯–◯) = 104
- ◯×(◯+◯)–◯² = 104

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

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