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

Study the seven clues below and place the numbers 1-9 into the nine positions. Each number should appear exactly once in this grid.

**x x x**

**x x x**

**x x x**

Clues:

- The 1 is directly left of the 9,
- The 9 is directly above the 6,
- The 6 is further right than the 4,
- The 4 is directly right of the 8,
- The 8 is directly above the 2,
- The 2 directly left of the 5,
- The 5 is not next to the 7.

**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 & 3rd rows contain the following fourteen numbers:

2 9 13 14 15 22 25 36 40 42 45 66 72 80

What is the difference between the highest and lowest 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 is only ONE way of making **96 **when using *Lagrange’s Theorem*. Can you find it?

**The Mathematically Possible Challenge**

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

9 18 27 36 45 54 63 72 81 90

#*9TimesTable*

**The Target Challenge**

Can you arrive at **96** by inserting **2**, **3**, **5** and **6** into the gaps on each line?

- (◯+◯)×◯×◯ = 96
- (◯×◯+◯)×◯ = 96
- ◯³+◯²+◯–◯² = 96
- (◯+◯)²–(◯+◯)² = 96
- (◯+◯)²+◯²–◯² = 96

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

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