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

Can you place the numbers **1 2 3 4 5 6 8 9 10 11 12** and **13** into the 12 gaps below so all four lines work out arithmetically?

◯ + ◯ = ◯

◯ + ◯ = ◯

◯ + ◯ = ◯

◯ + ◯ = ◯

Click this **Mathelona** link for details of similar challenges.

**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 3rd & 4th rows contain the following fourteen numbers:

3 10 13 25 32 35 36 42 44 45 54 60 66 80

List THREE different numbers that have a sum of 100.

**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 EIGHT ways of making **114 **when using *Lagrange’s Theorem*. Can you find them all?

**The Mathematically Possible Challenge**

Using **1**, **4** and **9 **once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

30 31 32 33 34 35 36 37 38 39

#*NumbersIn30s*

**The Target Challenge**

Can you arrive at **114** by inserting **3**, **6**, **12** and **16** into the gaps on both lines?

- (◯+◯)×(◯–◯) = 114
- ◯²–◯×(◯–◯) = 114

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

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