**The Main Challenge**

Here’s a 10-step number trail involving the four arithmetical operations, some 3-digit numbers, plus fractions and percentages.

Start with the number 2, then:

- add three hundred and eighty
- –292
- +106
- –50%
- 1/2 of this
- multiply by nine
- 1/3 of this
- –7
- divide by seven
- +7

What’s your answer?

**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 6th & 7th rows of the playing board contain the following fourteen numbers:

4 5 11 12 18 20 24 27 30 33 49 56 70 77

What is half of the highest even number?

**T****he 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).

Show how you can make **196**, in TEN different ways, when using *Lagrange’s Theorem*.

**The Mathematically Possible Challenge**

Based on our best-selling arithmetic board game.

Using **3**, **4** and **12** once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

1 3 6 10 15 21 28 36 45 55 66

#*TriangularNumbers*

**The Target ****Challeng****e**

Can you arrive at **196** by inserting **5**, **6**, **8** and **9** into the gaps on each line?

- (◯+◯)×(◯+◯) = 196
- (◯+◯)²+(◯×half◯) = 196
- (◯+◯)²–(◯²+half◯) = 196
- ◯³+◯–(◯+double◯) = 196
- ◯³+◯–(◯²+√◯) = 196

**Answers **can be found **here**.

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