**Th****e Main Challenge**

In this addition-only **Mathelona**-style puzzle, place the following 12 numbers into the 12 gaps so that all four lines work out:

1 1 2 3 4 4 5 5 6 8 9 10

◯ + ◯ = ◯

◯ + ◯ = ◯

◯ + ◯ = ◯

◯ + ◯ = ◯

**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 5th & 7th rows contain the following fourteen numbers:

4 6 7 11 16 21 24 27 30 50 70 77 81 84

From the list, what is the sum of the even numbers?

**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 **34 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **2**, **6** and **11 **once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

10 20 30 40 50 60 70 80 90 100

#*10TimesTable*

**The Target Challenge**

Can you arrive at **34** by inserting **2**, **3**, **5** and **8** into the gaps on each line?

- ◯×◯+◯×◯ = 34
- ◯×◯–◯×◯ = 34
- (◯–◯)²×◯+◯ = 34

**A****nsw****ers **can be found **here**.

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