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

You must arrive at the target number of **24** by using four unique numbers from **10-19** and with + – × ÷ available to use; one such example being (15×12÷18)+14 = 24.

Can you derive another 4-number combination to make 24?

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

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

How many cube numbers are present?

**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 are FOUR ways of making **65 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **1**, **6** and **7 **once each, with + – × ÷ available, which FIVE numbers is it possible to make from the list below?

40 41 42 43 44 45 46 47 48 49

#*NumbersIn40s*

**The Target Challenge**

Can you arrive at **65** by inserting **1**, **5**, **6** and **8** into the gaps on each line?

- (◯+◯–◯)×◯ = 65
- ◯×◯+(◯–◯)² = 65
- ◯²+(◯+◯)÷◯ = 65
- ◯²+◯–◯×◯ = 65

**A****nswers **can be found **here**.

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