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

Find the sum of all the numbers between **5 and 25** that are divisible by **3**, **4** or **7**.

**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, when 4 is subtracted from it, becomes a multiple of 15?

**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 **167**, in FIVE different ways, when using *Lagrange’s Theorem*.

**The Mathematically Possible Challenge**

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

6 12 18 24 30 36 42 48 54 60

#*6TimesTable*

**The Target Challenge**

Can you arrive at **167** by inserting **8**, **9**, **10** and **15** into the gaps on each line?

- ◯×◯+◯+◯ = 167
- ³√◯×◯²+◯–◯ = 167

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

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