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

Here’s a 7-part challenge to test your basic arithmetic knowledge:

- What is 56 divided by 14?
- (1 + 11) + (20 – 4) = ?
- Find which one of these is a factor of 14. Is it 3, 5, 7 or 10?
- What is the next number? 15, 30, 45, 60, …
- 10,000 × 0.001 = ?
- (2 + 3) – (4 – 9) = ?
- What is the sum of 0.81 and 0.5?

Can you get 7 out of 7 correct?

**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

Find THREE sets of three different numbers that have a sum of 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 FIVE ways of making **103 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **5**, **7** and **10 **once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

50 51 52 53 54 55 56 57 58 59

#*NumbersIn50s*

**The Target Challenge**

Can you arrive at **103** by inserting **1**, **2**, **6** and **8** into the gaps on both lines?

- ◯²+◯²+◯²–◯² = 103
- (◯+◯+◯)²–half(◯²) = 103

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

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