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

Place the 12 numbers **1 1 2 2 3 3 4 4 5 6 7** and **8** into the 12 gaps below so all three lines work out:

◯ + ◯ = 5 = ◯ – ◯

◯ + ◯ = 9 = ◯ × ◯

◯ + ◯ = 8 = ◯ ÷ ◯

Can you complete this **Mathelona** challenge?

**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 four different numbers from the list 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 FOUR ways of making **57 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

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

4 8 12 16 20 24 28 32 36 40

#*4TimesTable*

**The Target Challenge**

Can you arrive at** 57** by inserting **3**, **4**, **6** and **11** into the gaps in both lines?

- ◯×◯+◯×◯ = 57
- (◯+◯+√◯)×◯ = 57

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

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