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

Three DIFFERENT digits from **1-9** must be used in a particular way to arrive at a specified target number. The rule is to multiply two numbers together, then either add or subtract the third number, so you arrive at today’s target number of **30**.

As an example, one such way of making 30 is (8×3)+6. Can you find the other FOUR ways of making **30**?

[Note: (8×3)+6 = 30 and (3×8)+6 = 30 counts as just ONE way]

**T****he**** 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 4th & 6th rows contain the following fourteen numbers:

3 5 10 12 18 20 32 33 35 44 49 54 56 60

Which THREE numbers, when 31 is added to each, all become square numbers?

**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** (4+1+1+1).

Show how you can make **161**, in SEVEN different ways, when using *Lagrange’s Theorem*.

**The Mathematically Possible Challenge**

Using the three digits **3**, **5** and **8** once each, with + – × ÷ available, which SIX numbers is it possible to make from the list below?

1 4 9 16 25 36 49 64 81 100

#*SquareNumbers*

**The Target Challenge**

Can you arrive at **161** by inserting **3**, **8**, **10** and **15** into the gaps on each line?

- ◯×◯+◯+◯ = 161
- (◯+◯)×(◯–◯) = 161

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

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