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

Three unique digits from **1-9** must be used to arrive at the target number **18** when multiplying two numbers together and adding or subtracting the third unique number, **(a×b)±c**.

One way of arriving at 18 is (5×4)–2. Find the other FOUR ways it is possible to make **18**.

[Note: (5×4)–2 = 18 and (4×5)–2 = 18 counts as just ONE way.]

**The**** 7puzzle Challenge**

The playing board of **the 7puzzle game** is a 7-by-7 grid of 49 different numbers, ranging from **2 **up to **84**.

The 2nd & 7th rows contain the following fourteen numbers:

4 8 11 17 24 27 28 30 48 55 63 64 70 77

Which number above 20 becomes a multiple of 11 when 20 is subtracted from it?

**The Lagrange Challenge**

*Lagrange’s Four-Square Theorem* states that every 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 **169**, in EIGHT different ways, when using *Lagrange’s Theorem*.

**The Mathematically Possible Challenge**

Using **4**, **6** and **10** once each, with + – × ÷ available, which are the only FOUR numbers it’s possible to make from the list below?

8 16 24 32 40 48 56 64 72 80

#*8TimesTable*

**The Target Challenge**

Can you arrive at **169** by inserting **1**, **3**, **13** and **15** into the gaps on each line?

- ◯×(◯+◯–◯) = 169
- (◯–◯)²+(◯÷◯)² = 169

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

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