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

Can you arrive at the target answer of **24** by using each of the four numbers **1**, **7**, **13** and **13** exactly once each, and with + – × ÷ available?

**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 2nd & 4th rows contain the following fourteen numbers:

3 8 10 17 28 32 35 44 48 54 55 60 63 64

Which three different numbers from the list, when added together, make a total of 77?

**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 **24 **when using *Lagrange’s Theorem*. Can you find it?

**The Mathematically Possible Challenge**

Using **5**, **6** and **8 **once each, with + – × ÷ available, which are the only TWO numbers it is 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 **24** by inserting **2**, **3**, **6** and **8** into the gaps on each line?

- ◯×◯+◯–◯ = 24
- (◯–◯)²×◯×◯ = 24
- (◯+◯)×◯–◯ = 24

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

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